149:@0.890754:0.963104:0.932133:0.963104:0.932133:0.941283:0.890754:0.941283:0.000000:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.837761:0.967458:0.879897:0.967458:0.879897:0.954794:0.837761:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cción y expresión:@0.117728:0.244375:0.242599:0.244375:0.242599:0.229011:0.117728:0.229011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.096132:0.245161:0.108221:0.245161:0.108221:0.228025:0.096132:0.228025:0.000000
2.:@0.096353:0.565264:0.110579:0.565264:0.110579:0.548363:0.096353:0.548363:0.000000:0.000000
  Dado el plano :@0.110579:0.565264:0.232036:0.565264:0.232036:0.548875:0.110579:0.548875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∏=:@0.234818:0.563921:0.269332:0.563921:0.269332:0.546979:0.234818:0.546979:0.000000:0.000000
{:@0.271988:0.568566:0.280833:0.568566:0.280833:0.538884:0.271988:0.538884:0.000000
=:@0.294394:0.563921:0.304511:0.563921:0.304511:0.546979:0.294394:0.546979:0.000000
+ +=:@0.381409:0.563921:0.445079:0.563921:0.445079:0.546979:0.381409:0.546979:0.000000:0.000000:0.000000:0.000000
1:@0.249791:0.566340:0.255002:0.566340:0.255002:0.556842:0.249791:0.556842:0.000000
6} , encontremos::@0.448881:0.564336:0.575374:0.565266:0.575374:0.548877:0.448881:0.547947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.281558:0.564336:0.289022:0.564336:0.289022:0.547975:0.281558:0.547975:0.000000
x yz x:@0.314378:0.564336:0.376885:0.564336:0.376885:0.547975:0.314378:0.547975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.396234:0.564336:0.403715:0.564336:0.403715:0.547975:0.396234:0.547975:0.000000
z:@0.422456:0.564336:0.429698:0.564336:0.429698:0.547975:0.422456:0.547975:0.000000
(, ,)|:@0.307762:0.564336:0.365414:0.564336:0.365414:0.547947:0.307762:0.547947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.124855:0.588985:0.139763:0.588985:0.139763:0.572085:0.124855:0.572085:0.000000:0.000000
  El vector normal al plano.:@0.139763:0.588985:0.338188:0.588985:0.338188:0.572596:0.139763:0.572596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.124855:0.608514:0.141071:0.608514:0.141071:0.591613:0.124855:0.591613:0.000000:0.000000
  Determinemos si el plano :@0.141071:0.608514:0.344879:0.608514:0.344879:0.592125:0.141071:0.592125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∏=:@0.347362:0.606607:0.384070:0.606607:0.384070:0.589665:0.347362:0.589665:0.000000:0.000000
=:@0.409131:0.606607:0.419248:0.606607:0.419248:0.589665:0.409131:0.589665:0.000000
+:@0.504513:0.606607:0.514629:0.606607:0.514629:0.589665:0.504513:0.589665:0.000000
+:@0.539691:0.606607:0.549808:0.606607:0.549808:0.589665:0.539691:0.589665:0.000000
=:@0.574814:0.606607:0.584931:0.606607:0.584931:0.589665:0.574814:0.589665:0.000000
{:@0.386730:0.611253:0.395575:0.611253:0.395575:0.581570:0.386730:0.581570:0.000000
}:@0.604416:0.611253:0.613261:0.611253:0.613261:0.581570:0.604416:0.581570:0.000000
2:@0.363015:0.609028:0.368227:0.609028:0.368227:0.599529:0.363015:0.599529:0.000000
2 |:@0.482743:0.607022:0.480183:0.607022:0.480183:0.590633:0.482743:0.590633:0.000000:0.000000:0.000000
2:@0.517663:0.607022:0.526656:0.607022:0.526656:0.590633:0.517663:0.590633:0.000000
2:@0.552842:0.607022:0.561834:0.607022:0.561834:0.590633:0.552842:0.590633:0.000000
10  es paralelo al :@0.587338:0.607022:0.716554:0.608516:0.716554:0.592127:0.587338:0.590633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.396319:0.607022:0.403782:0.607022:0.403782:0.590661:0.396319:0.590661:0.000000
x yz:@0.429139:0.607022:0.467229:0.607022:0.467229:0.590661:0.429139:0.590661:0.000000:0.000000:0.000000:0.000000
x:@0.492548:0.607022:0.500011:0.607022:0.500011:0.590661:0.492548:0.590661:0.000000
y:@0.527726:0.607022:0.535208:0.607022:0.535208:0.590661:0.527726:0.590661:0.000000
z:@0.562334:0.607022:0.569576:0.607022:0.569576:0.590661:0.562334:0.590661:0.000000
(, ,):@0.422505:0.607022:0.473826:0.607022:0.473826:0.590633:0.422505:0.590633:0.000000:0.000000:0.000000:0.000000:0.000000
plano anterior.:@0.153369:0.625112:0.259326:0.625112:0.259326:0.608724:0.153369:0.608724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c):@0.124880:0.645277:0.138701:0.645277:0.138701:0.628376:0.124880:0.628376:0.000000:0.000000
  ¿Existe un plano perpendicular al plano dado?, ¿cuál podría ser su vector normal?:@0.138701:0.645277:0.712537:0.645277:0.712537:0.628888:0.138701:0.628888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1. :@0.102121:0.325058:0.157756:0.325058:0.157756:0.309480:0.102121:0.309480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es el vector normal al plano :@0.157756:0.325058:0.384798:0.325058:0.384798:0.310159:0.157756:0.310159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que representa la montaña?:@0.102121:0.340145:0.288894:0.340145:0.288894:0.325246:0.102121:0.325246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ecuación del plano es: :@0.102121:0.358791:0.272912:0.358791:0.272912:0.343892:0.102121:0.343892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3x − 2y + z = 6:@0.198263:0.377437:0.296064:0.377437:0.296064:0.362538:0.198263:0.362538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El vector normal al plano es: :@0.102121:0.397868:0.292176:0.397868:0.292176:0.382969:0.102121:0.382969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.294670:0.397652:0.303228:0.397652:0.303228:0.382926:0.294670:0.382926:0.000000
:@0.295334:0.387544:0.302134:0.387544:0.302134:0.372471:0.295334:0.372471:0.000000
=:@0.306446:0.397278:0.315551:0.397278:0.315551:0.382030:0.306446:0.382030:0.000000
−:@0.336033:0.397278:0.345138:0.397278:0.345138:0.382030:0.336033:0.382030:0.000000
(,32:@0.318453:0.397652:0.353165:0.397652:0.353165:0.382902:0.318453:0.382902:0.000000:0.000000:0.000000:0.000000
,):@0.352850:0.397652:0.366533:0.397652:0.366533:0.382902:0.352850:0.382902:0.000000:0.000000
1:@0.356383:0.397652:0.364476:0.397652:0.364476:0.382902:0.356383:0.382902:0.000000
Es un vector perpendicular a la superficie :@0.102121:0.416534:0.379720:0.416534:0.379720:0.401635:0.102121:0.401635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la montaña.:@0.102121:0.431621:0.201748:0.431621:0.201748:0.416722:0.102121:0.416722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 2.:@0.403597:0.325053:0.455848:0.325053:0.455848:0.309475:0.403597:0.309475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.455848:0.325053:0.459232:0.325053:0.459232:0.309475:0.455848:0.309475:0.000000
¿Qué condición debe cumplir la :@0.459232:0.325053:0.676159:0.325053:0.676159:0.310154:0.459232:0.310154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dirección del vuelo respecto del vector :@0.403597:0.340140:0.666387:0.340140:0.666387:0.325241:0.403597:0.325241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
normal del plano?:@0.403597:0.355228:0.524231:0.355228:0.524231:0.340329:0.403597:0.340329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un vector   es paralelo al plano si es :@0.403597:0.373874:0.648052:0.373885:0.648052:0.358986:0.403597:0.358975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.472512:0.374061:0.479478:0.374061:0.479478:0.359336:0.472512:0.359336:0.000000
:@0.473408:0.364514:0.480208:0.364514:0.480208:0.349440:0.473408:0.349440:0.000000
=:@0.484288:0.373687:0.493393:0.373687:0.493393:0.358440:0.484288:0.358440:0.000000
−:@0.524804:0.373687:0.533909:0.373687:0.533909:0.358440:0.524804:0.358440:0.000000
(:@0.496589:0.375262:0.502112:0.375262:0.502112:0.355775:0.496589:0.355775:0.000000
):@0.540174:0.375262:0.545697:0.375262:0.545697:0.355775:0.540174:0.355775:0.000000
21 1:@0.502950:0.374061:0.541957:0.374061:0.541957:0.359311:0.502950:0.359311:0.000000:0.000000:0.000000:0.000000
,,:@0.510728:0.374061:0.522619:0.374061:0.522619:0.359311:0.510728:0.359311:0.000000:0.000000
perpendicular al vector normal.:@0.403601:0.388972:0.612350:0.388972:0.612350:0.374073:0.403601:0.374073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vn:@0.532362:0.408062:0.554768:0.408062:0.554768:0.393337:0.532362:0.393337:0.000000:0.000000
⋅=:@0.542578:0.407689:0.567091:0.407689:0.567091:0.392441:0.542578:0.392441:0.000000:0.000000
:@0.533390:0.397955:0.553673:0.397955:0.553673:0.382881:0.533390:0.382881:0.000000:0.000000:0.000000:0.000000
0:@0.570291:0.408062:0.578385:0.408062:0.578385:0.393312:0.570291:0.393312:0.000000
Es decir, el producto punto entre el vector de :@0.403601:0.423682:0.707585:0.423682:0.707585:0.408782:0.403601:0.408782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dirección del vuelo y vector normal del plano :@0.403601:0.438769:0.709078:0.438769:0.709078:0.423870:0.403601:0.423870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
debe ser cero.:@0.403601:0.453857:0.496743:0.453857:0.496743:0.438958:0.403601:0.438958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 3.:@0.102125:0.474891:0.154376:0.474891:0.154376:0.459313:0.102125:0.459313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.154376:0.474891:0.158045:0.474891:0.158045:0.459992:0.154376:0.459992:0.000000
Determina si el vector de dirección :@0.158045:0.474891:0.393848:0.474891:0.393848:0.459992:0.158045:0.459992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.395500:0.474634:0.402465:0.474634:0.402465:0.459909:0.395500:0.459909:0.000000
:@0.396396:0.465093:0.403196:0.465093:0.403196:0.450019:0.396396:0.450019:0.000000
=:@0.407276:0.474267:0.416381:0.474267:0.416381:0.459019:0.407276:0.459019:0.000000
−:@0.447793:0.474267:0.456898:0.474267:0.456898:0.459019:0.447793:0.459019:0.000000
(:@0.419576:0.475835:0.425099:0.475835:0.425099:0.456348:0.419576:0.456348:0.000000
):@0.463161:0.475835:0.468684:0.475835:0.468684:0.456348:0.463161:0.456348:0.000000
21 1:@0.425937:0.474634:0.464945:0.474634:0.464945:0.459884:0.425937:0.459884:0.000000:0.000000:0.000000:0.000000
,,:@0.433716:0.474634:0.445607:0.474634:0.445607:0.459884:0.433716:0.459884:0.000000:0.000000
 es paralelo al plano de la montaña. :@0.469822:0.474891:0.708828:0.474891:0.708828:0.459992:0.469822:0.459992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vn:@0.287641:0.496111:0.310047:0.496111:0.310047:0.481386:0.287641:0.481386:0.000000:0.000000
⋅=:@0.297857:0.495737:0.322370:0.495737:0.322370:0.480490:0.297857:0.480490:0.000000:0.000000
− ⋅:@0.353782:0.495737:0.380696:0.495737:0.380696:0.480490:0.353782:0.480490:0.000000:0.000000:0.000000
(:@0.325569:0.497311:0.331091:0.497311:0.331091:0.477824:0.325569:0.477824:0.000000
) (:@0.369154:0.497311:0.387914:0.497311:0.387914:0.477824:0.369154:0.477824:0.000000:0.000000:0.000000
−:@0.401609:0.495737:0.410714:0.495737:0.410714:0.480490:0.401609:0.480490:0.000000
):@0.428281:0.497311:0.433804:0.497311:0.433804:0.477824:0.428281:0.477824:0.000000
=− −=:@0.437235:0.495737:0.511403:0.495737:0.511403:0.480490:0.437235:0.480490:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.288676:0.486003:0.308960:0.486003:0.308960:0.470929:0.288676:0.470929:0.000000:0.000000:0.000000:0.000000
21 1:@0.331929:0.496111:0.370937:0.496111:0.370937:0.481361:0.331929:0.481361:0.000000:0.000000:0.000000:0.000000
3 21:@0.388766:0.496111:0.430079:0.496111:0.430079:0.481361:0.388766:0.481361:0.000000:0.000000:0.000000:0.000000
62 13:@0.449782:0.496111:0.522688:0.496111:0.522688:0.481361:0.449782:0.481361:0.000000:0.000000:0.000000:0.000000:0.000000
,,:@0.339704:0.496111:0.351596:0.496111:0.351596:0.481361:0.339704:0.481361:0.000000:0.000000
,:@0.396524:0.496111:0.399410:0.496111:0.399410:0.481361:0.396524:0.481361:0.000000
,:@0.418433:0.496111:0.421318:0.496111:0.421318:0.481361:0.418433:0.481361:0.000000
El producto punto no es cero, por lo tanto, la ruta de vuelo no es paralela al plano de la :@0.102121:0.515105:0.682974:0.515105:0.682974:0.500206:0.102121:0.500206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
montaña y no es segura.:@0.102121:0.530193:0.265256:0.530193:0.265256:0.515293:0.102121:0.515293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1.:@0.102121:0.669547:0.154372:0.669547:0.154372:0.653969:0.102121:0.653969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.154372:0.669547:0.158041:0.669547:0.158041:0.654648:0.154372:0.654648:0.000000
Dado el plano::@0.158041:0.669547:0.254736:0.669547:0.254736:0.654648:0.158041:0.654648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∏=:@0.301294:0.685048:0.332358:0.685048:0.332358:0.669800:0.301294:0.669800:0.000000:0.000000
{:@0.334747:0.689228:0.342708:0.689228:0.342708:0.662514:0.334747:0.662514:0.000000
=:@0.354914:0.685048:0.364019:0.685048:0.364019:0.669800:0.354914:0.669800:0.000000
+ +=:@0.433228:0.685048:0.490529:0.685048:0.490529:0.669800:0.433228:0.669800:0.000000:0.000000:0.000000:0.000000
1:@0.314770:0.687225:0.319461:0.687225:0.319461:0.678676:0.314770:0.678676:0.000000
6}:@0.493954:0.685421:0.506931:0.685421:0.506931:0.670671:0.493954:0.670671:0.000000:0.000000
x:@0.343363:0.685421:0.350080:0.685421:0.350080:0.670696:0.343363:0.670696:0.000000
x yz x:@0.372901:0.685421:0.429157:0.685421:0.429157:0.670696:0.372901:0.670696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.446571:0.685421:0.453304:0.685421:0.453304:0.670696:0.446571:0.670696:0.000000
z:@0.470171:0.685421:0.476689:0.685421:0.476689:0.670696:0.470171:0.670696:0.000000
(, ,)|:@0.366947:0.685421:0.418832:0.685421:0.418832:0.670671:0.366947:0.670671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El vector normal al plano es: :@0.102121:0.707596:0.292176:0.707596:0.292176:0.692697:0.102121:0.692697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.294454:0.707705:0.303012:0.707705:0.303012:0.692979:0.294454:0.692979:0.000000
:@0.295118:0.697585:0.301918:0.697585:0.301918:0.682511:0.295118:0.682511:0.000000
1:@0.302229:0.706962:0.306920:0.706962:0.306920:0.698414:0.302229:0.698414:0.000000
1, 1, 1):@0.326388:0.707705:0.366805:0.707705:0.366805:0.692955:0.326388:0.692955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.310715:0.707331:0.319820:0.707331:0.319820:0.692083:0.310715:0.692083:0.000000
(:@0.322723:0.707705:0.327118:0.707705:0.327118:0.692955:0.322723:0.692955:0.000000
Paso 2.:@0.102121:0.726570:0.154372:0.726570:0.154372:0.710992:0.102121:0.710992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.154372:0.726570:0.158041:0.726570:0.158041:0.711671:0.154372:0.711671:0.000000
Verificamos si el vector:@0.157454:0.726570:0.308893:0.726570:0.308893:0.711671:0.157454:0.711671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∏=:@0.219913:0.745708:0.252950:0.745708:0.252950:0.730460:0.219913:0.730460:0.000000:0.000000
{:@0.255344:0.749888:0.263305:0.749888:0.263305:0.723174:0.255344:0.723174:0.000000
=:@0.275511:0.745708:0.284616:0.745708:0.284616:0.730460:0.275511:0.730460:0.000000
+:@0.361354:0.745708:0.370459:0.745708:0.370459:0.730460:0.361354:0.730460:0.000000
+:@0.393015:0.745708:0.402120:0.745708:0.402120:0.730460:0.393015:0.730460:0.000000
=:@0.424625:0.745708:0.433730:0.745708:0.433730:0.730460:0.424625:0.730460:0.000000
2:@0.234002:0.747885:0.238692:0.747885:0.238692:0.739336:0.234002:0.739336:0.000000
2 |:@0.341755:0.746081:0.339429:0.746081:0.339429:0.731331:0.341755:0.731331:0.000000:0.000000:0.000000
2:@0.373183:0.746081:0.381277:0.746081:0.381277:0.731331:0.373183:0.731331:0.000000
2:@0.404844:0.746081:0.412938:0.746081:0.412938:0.731331:0.404844:0.731331:0.000000
10}:@0.435891:0.746081:0.456867:0.746081:0.456867:0.731331:0.435891:0.731331:0.000000:0.000000:0.000000
x:@0.263973:0.746081:0.270690:0.746081:0.270690:0.731356:0.263973:0.731356:0.000000
x yz:@0.293511:0.746081:0.327792:0.746081:0.327792:0.731356:0.293511:0.731356:0.000000:0.000000:0.000000:0.000000
x:@0.350579:0.746081:0.357296:0.746081:0.357296:0.731356:0.350579:0.731356:0.000000
y:@0.382240:0.746081:0.388973:0.746081:0.388973:0.731356:0.382240:0.731356:0.000000
z:@0.413386:0.746081:0.419904:0.746081:0.419904:0.731356:0.413386:0.731356:0.000000
(, ,):@0.287540:0.746081:0.333729:0.746081:0.333729:0.731331:0.287540:0.731331:0.000000:0.000000:0.000000:0.000000:0.000000
 es paralelo al dado.:@0.460159:0.746727:0.591262:0.746727:0.591262:0.731828:0.460159:0.731828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El vector normal al plano es:      :@0.102127:0.767599:0.310525:0.767599:0.310525:0.752700:0.102127:0.752700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.311364:0.767392:0.319922:0.767392:0.319922:0.752667:0.311364:0.752667:0.000000
:@0.312028:0.757273:0.318827:0.757273:0.318827:0.742199:0.312028:0.742199:0.000000
2:@0.319752:0.766650:0.324443:0.766650:0.324443:0.758101:0.319752:0.758101:0.000000
2, 2, 2):@0.346325:0.767392:0.388517:0.767392:0.388517:0.752642:0.346325:0.752642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.329591:0.767019:0.338696:0.767019:0.338696:0.751771:0.329591:0.751771:0.000000
(:@0.341598:0.767392:0.345993:0.767392:0.345993:0.752642:0.341598:0.752642:0.000000
Observamos que: :@0.102121:0.786248:0.222837:0.786248:0.222837:0.771349:0.102121:0.771349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.228679:0.785729:0.237237:0.785729:0.237237:0.771004:0.228679:0.771004:0.000000
n:@0.266228:0.785729:0.274785:0.785729:0.274785:0.771004:0.266228:0.771004:0.000000
2:@0.236324:0.787524:0.241014:0.787524:0.241014:0.778975:0.236324:0.778975:0.000000
1:@0.273261:0.787524:0.277952:0.787524:0.277952:0.778975:0.273261:0.778975:0.000000
2 ;   (2, 2, 2) = 2(1, 1, 1):@0.258469:0.785729:0.410727:0.785729:0.410727:0.770979:0.258469:0.770979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.246172:0.785355:0.255277:0.785355:0.255277:0.770108:0.246172:0.770108:0.000000
Los planos son paralelos porque sus vectores normales son proporcionales.:@0.102121:0.804900:0.602055:0.804900:0.602055:0.790001:0.102121:0.790001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 3.:@0.102121:0.822880:0.154171:0.822880:0.154171:0.807302:0.102121:0.807302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.154171:0.822880:0.157840:0.822880:0.157840:0.807981:0.154171:0.807981:0.000000
Determinamos si existe un plano perpendicular al plano dado, y ¿cuál podría ser su :@0.157622:0.822880:0.710198:0.822880:0.710198:0.807981:0.157622:0.807981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector normal?:@0.102121:0.837967:0.202165:0.837967:0.202165:0.823068:0.102121:0.823068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Debemos determinar un vector que sea perpendicular al vector normal del plano:@0.102121:0.858398:0.644254:0.858398:0.644254:0.843499:0.102121:0.843499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.104403:0.879916:0.112960:0.879916:0.112960:0.865191:0.104403:0.865191:0.000000
:@0.105066:0.869796:0.111866:0.869796:0.111866:0.854723:0.105066:0.854723:0.000000
1:@0.112177:0.879173:0.116867:0.879173:0.116867:0.870625:0.112177:0.870625:0.000000
1, 1, 1):@0.136335:0.879916:0.176753:0.879916:0.176753:0.865166:0.136335:0.865166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.120662:0.879542:0.129768:0.879542:0.129768:0.864294:0.120662:0.864294:0.000000
(:@0.132670:0.879916:0.137065:0.879916:0.137065:0.865166:0.132670:0.865166:0.000000
 es decir:         :@0.178645:0.879986:0.269745:0.879986:0.269745:0.865087:0.178645:0.865087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nv:@0.275007:0.879666:0.295506:0.879666:0.295506:0.866401:0.275007:0.866401:0.000000:0.000000
ab c:@0.414723:0.879666:0.444829:0.879666:0.444829:0.866401:0.414723:0.866401:0.000000:0.000000:0.000000:0.000000
a bc:@0.465732:0.879666:0.513843:0.879666:0.513843:0.866401:0.465732:0.866401:0.000000:0.000000:0.000000:0.000000
:@0.275574:0.870550:0.296134:0.870550:0.296134:0.856970:0.275574:0.856970:0.000000:0.000000
⋅=:@0.284196:0.879330:0.308027:0.879330:0.308027:0.865593:0.284196:0.865593:0.000000:0.000000
⋅:@0.401948:0.879330:0.405683:0.879330:0.405683:0.865593:0.401948:0.865593:0.000000
⇒:@0.332023:0.879330:0.346770:0.879330:0.346770:0.865593:0.332023:0.865593:0.000000
(:@0.408779:0.880741:0.376148:0.880741:0.376148:0.863186:0.408779:0.863186:0.000000
):@0.446387:0.880741:0.413755:0.880741:0.413755:0.863186:0.446387:0.863186:0.000000
= + +=:@0.454451:0.879330:0.525976:0.879330:0.525976:0.865593:0.454451:0.865593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0   :@0.310912:0.879666:0.328662:0.879666:0.328662:0.866378:0.310912:0.866378:0.000000:0.000000:0.000000:0.000000
1, 1, 1):@0.360442:0.879801:0.398573:0.879666:0.398573:0.866378:0.360442:0.866513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.528846:0.879666:0.536137:0.879666:0.536137:0.866378:0.528846:0.866378:0.000000
  (:@0.350342:0.879666:0.361100:0.879666:0.361100:0.866378:0.350342:0.866378:0.000000:0.000000:0.000000
,,:@0.422449:0.879666:0.436897:0.879666:0.436897:0.866378:0.422449:0.866378:0.000000:0.000000
Los posibles vectores deben cumplir con esta condición. :@0.102121:0.898638:0.482483:0.898638:0.482483:0.883739:0.102121:0.883739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos: :@0.102121:0.919145:0.169901:0.919145:0.169901:0.904246:0.102121:0.904246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.172019:0.919404:0.178985:0.919404:0.178985:0.904679:0.172019:0.904679:0.000000
:@0.172915:0.909297:0.179715:0.909297:0.179715:0.894224:0.172915:0.894224:0.000000
=:@0.183795:0.919031:0.192900:0.919031:0.192900:0.903783:0.183795:0.903783:0.000000
−:@0.210032:0.919031:0.219137:0.919031:0.219137:0.903783:0.210032:0.903783:0.000000
(,11:@0.195802:0.919404:0.227181:0.919404:0.227181:0.904654:0.195802:0.904654:0.000000:0.000000:0.000000:0.000000
,):@0.224544:0.919404:0.242091:0.919404:0.242091:0.904654:0.224544:0.904654:0.000000:0.000000
0:@0.229121:0.919404:0.237215:0.919404:0.237215:0.904654:0.229121:0.904654:0.000000
 otro vector :@0.245286:0.919151:0.326217:0.919151:0.326217:0.904252:0.245286:0.904252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.328336:0.919086:0.335302:0.919086:0.335302:0.904360:0.328336:0.904360:0.000000
:@0.329232:0.908978:0.336031:0.908978:0.336031:0.893905:0.329232:0.893905:0.000000
=:@0.340111:0.918712:0.349216:0.918712:0.349216:0.903464:0.340111:0.903464:0.000000
− −:@0.369699:0.918712:0.398407:0.918712:0.398407:0.903464:0.369699:0.903464:0.000000:0.000000:0.000000
(,21 1:@0.352135:0.919086:0.406451:0.919086:0.406451:0.904335:0.352135:0.904335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.384227:0.919086:0.387113:0.919086:0.387113:0.904335:0.384227:0.904335:0.000000
):@0.404112:0.919086:0.408507:0.919086:0.408507:0.904335:0.404112:0.904335:0.000000
.:@0.410647:0.919151:0.413562:0.919151:0.413562:0.904252:0.410647:0.904252:0.000000
Ejemplos paso a paso:@0.096356:0.270472:0.251248:0.270472:0.251248:0.255107:0.096356:0.255107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.096359:0.298076:0.110585:0.298076:0.110585:0.281175:0.096359:0.281175:0.000000:0.000000
  Resolvamos el problema inicial.:@0.110585:0.298076:0.353790:0.298076:0.353790:0.281687:0.110585:0.281687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.096359:0.096845:0.113018:0.096845:0.113018:0.079709:0.096359:0.079709:0.000000:0.000000
 :@0.113018:0.096845:0.117053:0.096845:0.117053:0.080456:0.113018:0.080456:0.000000
Planos perpendiculares: :@0.124848:0.096845:0.319995:0.096845:0.319995:0.079944:0.124848:0.079944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos planos son perpendiculares si el producto punto :@0.320658:0.096845:0.716578:0.096845:0.716578:0.080456:0.320658:0.080456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o escalar de los vectores normales es cero.:@0.124848:0.113441:0.433837:0.113441:0.433837:0.097052:0.124848:0.097052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.134007:0.100395:0.134007:0.100395:0.117618:0.096359:0.117618:0.000000
n:@0.337691:0.133732:0.347199:0.133732:0.347199:0.117370:0.337691:0.117370:0.000000
n:@0.371726:0.133732:0.381235:0.133732:0.381235:0.117370:0.371726:0.117370:0.000000
nn:@0.434491:0.133732:0.466242:0.133732:0.466242:0.117370:0.434491:0.117370:0.000000:0.000000
:@0.338428:0.122501:0.345983:0.122501:0.345983:0.105753:0.338428:0.105753:0.000000
:@0.372464:0.122501:0.380019:0.122501:0.380019:0.105753:0.372464:0.105753:0.000000
 :@0.435062:0.122501:0.465026:0.122501:0.465026:0.105753:0.435062:0.105753:0.000000:0.000000:0.000000:0.000000
1:@0.346328:0.132907:0.351540:0.132907:0.351540:0.123408:0.346328:0.123408:0.000000
2:@0.381037:0.132907:0.386249:0.132907:0.386249:0.123408:0.381037:0.123408:0.000000
1:@0.442285:0.135736:0.447497:0.135736:0.447497:0.126238:0.442285:0.126238:0.000000
2:@0.466047:0.132907:0.471259:0.132907:0.471259:0.123408:0.466047:0.123408:0.000000
0:@0.490662:0.133732:0.499654:0.133732:0.499654:0.117343:0.490662:0.117343:0.000000
⊥:@0.355753:0.133317:0.367878:0.133317:0.367878:0.116375:0.355753:0.116375:0.000000
⇔:@0.401509:0.133317:0.420710:0.133317:0.420710:0.116375:0.401509:0.116375:0.000000
⋅:@0.449992:0.133317:0.454599:0.133317:0.454599:0.116375:0.449992:0.116375:0.000000
=:@0.477007:0.133317:0.487124:0.133317:0.487124:0.116375:0.477007:0.116375:0.000000
  :@0.388683:0.133732:0.396755:0.133732:0.396755:0.117343:0.388683:0.117343:0.000000:0.000000
  :@0.425539:0.133732:0.433610:0.133732:0.433610:0.117343:0.425539:0.117343:0.000000:0.000000
 :@0.096359:0.154407:0.100395:0.154407:0.100395:0.138018:0.096359:0.138018:0.000000
Por ejemplo, el vector normal del plano   es: :@0.124848:0.154407:0.460784:0.154407:0.460784:0.138018:0.124848:0.138018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.423026:0.154407:0.432921:0.154407:0.432921:0.138045:0.423026:0.138045:0.000000
n:@0.462454:0.154179:0.471963:0.154179:0.471963:0.137818:0.462454:0.137818:0.000000
:@0.463191:0.142949:0.470747:0.142949:0.470747:0.126200:0.463191:0.126200:0.000000
1:@0.471093:0.153354:0.476305:0.153354:0.476305:0.143856:0.471093:0.143856:0.000000
12 1) y el vector normal del :@0.497949:0.154179:0.716526:0.154407:0.716526:0.138018:0.497949:0.137790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.480517:0.153764:0.490633:0.153764:0.490633:0.136822:0.480517:0.136822:0.000000
−:@0.523398:0.153764:0.533514:0.153764:0.533514:0.136822:0.523398:0.136822:0.000000
(,:@0.493858:0.154179:0.507218:0.154179:0.507218:0.137790:0.493858:0.137790:0.000000:0.000000
,:@0.517722:0.154179:0.520928:0.154179:0.520928:0.137790:0.517722:0.137790:0.000000
plano   es :@0.124855:0.171072:0.203743:0.171072:0.203743:0.154683:0.124855:0.154683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.171016:0.171072:0.179861:0.171072:0.179861:0.154711:0.171016:0.154711:0.000000
n:@0.204258:0.171023:0.213766:0.171023:0.213766:0.154662:0.204258:0.154662:0.000000
:@0.204995:0.159793:0.212550:0.159793:0.212550:0.143044:0.204995:0.143044:0.000000
2:@0.213575:0.170198:0.218787:0.170198:0.218787:0.160700:0.213575:0.160700:0.000000
210,) determinemos si los planos son perpendiculares.:@0.243102:0.171023:0.654289:0.171072:0.654289:0.154683:0.243102:0.154634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.224508:0.170608:0.234625:0.170608:0.234625:0.153666:0.224508:0.153666:0.000000
−:@0.257383:0.170608:0.267500:0.170608:0.267500:0.153666:0.257383:0.153666:0.000000
(,:@0.237850:0.171023:0.254932:0.171023:0.254932:0.154634:0.237850:0.154634:0.000000:0.000000
 :@0.096357:0.191306:0.100393:0.191306:0.100393:0.174917:0.096357:0.174917:0.000000
Calculamos el producto punto: :@0.124846:0.191306:0.355833:0.191306:0.355833:0.174917:0.124846:0.174917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nn:@0.356777:0.191243:0.389375:0.191243:0.389375:0.174882:0.356777:0.174882:0.000000:0.000000
:@0.357509:0.180013:0.388154:0.180013:0.388154:0.163264:0.357509:0.163264:0.000000:0.000000
1:@0.365414:0.190418:0.370626:0.190418:0.370626:0.180920:0.365414:0.180920:0.000000
2:@0.389187:0.190418:0.394399:0.190418:0.394399:0.180920:0.389187:0.180920:0.000000
12 12 10:@0.417556:0.191243:0.524234:0.191243:0.524234:0.174854:0.417556:0.174854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0, 2 – 2 + 0 = 0, :@0.549010:0.191243:0.663922:0.191298:0.663922:0.174909:0.549010:0.174854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.373119:0.190828:0.377726:0.190828:0.377726:0.173886:0.373119:0.173886:0.000000
=:@0.400134:0.190828:0.410250:0.190828:0.410250:0.173886:0.400134:0.173886:0.000000
−⋅:@0.443015:0.190828:0.470822:0.190828:0.470822:0.173886:0.443015:0.173886:0.000000:0.000000
−:@0.494059:0.190828:0.504176:0.190828:0.504176:0.173886:0.494059:0.173886:0.000000
(:@0.472681:0.192577:0.478818:0.192577:0.478818:0.170925:0.472681:0.170925:0.000000
):@0.525403:0.192577:0.531539:0.192577:0.531539:0.170925:0.525403:0.170925:0.000000
=:@0.535345:0.190828:0.545462:0.190828:0.545462:0.173886:0.535345:0.173886:0.000000
(,:@0.413472:0.191243:0.426832:0.191243:0.426832:0.174854:0.413472:0.174854:0.000000:0.000000
,:@0.437336:0.191243:0.440542:0.191243:0.440542:0.174854:0.437336:0.174854:0.000000
):@0.459430:0.191243:0.464314:0.191243:0.464314:0.174854:0.459430:0.174854:0.000000
,:@0.488380:0.191243:0.491587:0.191243:0.491587:0.174854:0.488380:0.174854:0.000000
,:@0.510162:0.191243:0.513368:0.191243:0.513368:0.174854:0.510162:0.174854:0.000000
los vectores son perpendiculares.:@0.124840:0.207895:0.367933:0.207895:0.367933:0.191506:0.124840:0.191506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rutas aéreas seguras:@0.754293:0.346158:0.904845:0.346158:0.904845:0.330793:0.754293:0.330793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si se desea que un avión :@0.754293:0.363546:0.921612:0.363546:0.921612:0.348647:0.754293:0.348647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vuele en paralelo a un :@0.754293:0.377376:0.905031:0.377376:0.905031:0.362477:0.754293:0.362477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
plano, se debe garantizar :@0.754293:0.391207:0.925083:0.391207:0.925083:0.376308:0.754293:0.376308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que el vector de su :@0.754293:0.405037:0.884960:0.405037:0.884960:0.390138:0.754293:0.390138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trayectoria sea ortogonal :@0.754293:0.418867:0.924529:0.418867:0.924529:0.403968:0.754293:0.403968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al vector normal.:@0.754293:0.432698:0.865510:0.432698:0.865510:0.417799:0.754293:0.417799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Así se evitan colisiones, ya :@0.754293:0.450086:0.930608:0.450086:0.930608:0.435187:0.754293:0.435187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que la trayectoria no corta :@0.754293:0.463916:0.933138:0.463916:0.933138:0.449017:0.754293:0.449017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la superficie del plano. :@0.754293:0.477747:0.906803:0.477747:0.906803:0.462848:0.754293:0.462848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta lógica se usa en :@0.754293:0.491577:0.893721:0.491577:0.893721:0.476678:0.754293:0.476678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simuladores, radares y :@0.754293:0.505407:0.904476:0.505407:0.904476:0.490508:0.754293:0.490508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sistemas de navegación :@0.754293:0.519238:0.916957:0.519238:0.916957:0.504339:0.754293:0.504339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para planificar rutas :@0.754293:0.533068:0.888362:0.533068:0.888362:0.518169:0.754293:0.518169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
seguras y eficientes.:@0.754293:0.546898:0.886449:0.546898:0.886449:0.531999:0.754293:0.531999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Investiga en qué otras :@0.754293:0.668228:0.895162:0.668228:0.895162:0.653354:0.754293:0.653354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
actividades se emplean :@0.754293:0.682058:0.905031:0.682058:0.905031:0.667184:0.754293:0.667184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estos vectores.:@0.754293:0.695888:0.843816:0.695888:0.843816:0.681015:0.754293:0.681015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Seguridad vial:@0.788896:0.313717:0.897453:0.313717:0.897453:0.296816:0.788896:0.296816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.947692:0.641230:0.947692:0.598404:0.935781:0.598404:0.935781:0.641230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000