148:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
Plano en el espacio:@0.287495:0.447658:0.480610:0.447658:0.480610:0.426148:0.287495:0.426148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un plano en el espacio tridimensional es una superficie plana infinita que se extiende :@0.287495:0.470439:0.907731:0.470439:0.907731:0.454050:0.287495:0.454050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.661411:0.470439:0.665446:0.470439:0.665446:0.454050:0.661411:0.454050:0.000000
 :@0.752462:0.470439:0.756497:0.470439:0.756497:0.454050:0.752462:0.454050:0.000000
en todas las direcciones, se define mediante la ecuación general que involucra las :@0.287495:0.487036:0.907749:0.487036:0.907749:0.470647:0.287495:0.470647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.520365:0.487036:0.524401:0.487036:0.524401:0.470647:0.520365:0.470647:0.000000
variables:  ,  ,  .:@0.287495:0.503632:0.398983:0.503632:0.398983:0.487243:0.287495:0.487243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.359105:0.503632:0.395776:0.503632:0.395776:0.487271:0.359105:0.487271:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuación general del plano:@0.287495:0.532744:0.521250:0.532744:0.521250:0.514307:0.287495:0.514307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ecuación general de un plano en el espacio tridimensional tiene la forma::@0.287495:0.556153:0.845442:0.556153:0.845442:0.539764:0.287495:0.539764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ax By Cz D:@0.524632:0.576193:0.639731:0.576193:0.639731:0.559832:0.524632:0.559832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.546432:0.575778:0.556549:0.575778:0.556549:0.558836:0.546432:0.558836:0.000000
+:@0.580468:0.575778:0.590585:0.575778:0.590585:0.558836:0.580468:0.558836:0.000000
+:@0.615057:0.575778:0.625173:0.575778:0.625173:0.558836:0.615057:0.558836:0.000000
=:@0.644486:0.575778:0.654602:0.575778:0.654602:0.558836:0.644486:0.558836:0.000000
0:@0.658141:0.576193:0.667133:0.576193:0.667133:0.559804:0.658141:0.559804:0.000000
Donde:  ,  ,   son los coeficientes que definen el :@0.287495:0.596475:0.665315:0.596475:0.665315:0.580086:0.287495:0.580086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.347090:0.596475:0.393583:0.596475:0.393583:0.580114:0.347090:0.580114:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.489276:0.596475:0.493312:0.596475:0.493312:0.580086:0.489276:0.580086:0.000000
 :@0.609572:0.596475:0.613607:0.596475:0.613607:0.580086:0.609572:0.580086:0.000000
vector normal al plano:@0.666992:0.596475:0.844449:0.596475:0.844449:0.579851:0.666992:0.579851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, que se :@0.844449:0.596475:0.907637:0.596475:0.907637:0.580086:0.844449:0.580086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representa como: :@0.287495:0.613140:0.419953:0.613140:0.419953:0.596752:0.287495:0.596752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.420826:0.613100:0.430335:0.613100:0.430335:0.596739:0.420826:0.596739:0.000000
A BC:@0.453590:0.613100:0.492989:0.613100:0.492989:0.596739:0.453590:0.596739:0.000000:0.000000:0.000000:0.000000
:@0.421563:0.601870:0.429119:0.601870:0.429119:0.585121:0.421563:0.585121:0.000000
=:@0.433910:0.612685:0.444026:0.612685:0.444026:0.595743:0.433910:0.595743:0.000000
(, ,):@0.447251:0.613100:0.499789:0.613100:0.499789:0.596711:0.447251:0.596711:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.287495:0.633301:0.299031:0.633301:0.299031:0.616940:0.287495:0.616940:0.000000
 es un número real que ajusta la posición del plano,  ,  ,   son las coordenadas de un :@0.299031:0.633301:0.907665:0.633301:0.907665:0.616912:0.299031:0.616912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.671398:0.633301:0.706779:0.633301:0.706779:0.616940:0.671398:0.616940:0.000000:0.000000:0.000000:0.000000:0.000000
punto cualquiera que pertenece al plano.:@0.287477:0.649898:0.591012:0.649898:0.591012:0.633509:0.287477:0.633509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vector normal al plano::@0.287477:0.670062:0.472140:0.670062:0.472140:0.653162:0.287477:0.653162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el vector normal es un vector perpendicular al plano.:@0.472140:0.670062:0.862672:0.670062:0.862672:0.653673:0.472140:0.653673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo:  dado el vector normal :@0.287477:0.690268:0.552465:0.690268:0.552465:0.673879:0.287477:0.673879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.553162:0.690218:0.562670:0.690218:0.562670:0.673857:0.553162:0.673857:0.000000
:@0.553899:0.678988:0.561454:0.678988:0.561454:0.662239:0.553899:0.662239:0.000000
=:@0.566245:0.689803:0.576362:0.689803:0.576362:0.672861:0.566245:0.672861:0.000000
−:@0.599120:0.689803:0.609237:0.689803:0.609237:0.672861:0.599120:0.672861:0.000000
(,21:@0.579587:0.690218:0.618156:0.690218:0.618156:0.673829:0.579587:0.673829:0.000000:0.000000:0.000000:0.000000
,) y el punto  (1, 0, 2) que pertenece al :@0.615244:0.690218:0.907642:0.690267:0.907642:0.673878:0.615244:0.673829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.620312:0.690218:0.629305:0.690218:0.629305:0.673829:0.620312:0.673829:0.000000
P:@0.716107:0.690267:0.724879:0.690267:0.724879:0.673906:0.716107:0.673906:0.000000
plano, entonces la ecuación del plano es: :@0.287500:0.706863:0.592200:0.706863:0.592200:0.690474:0.287500:0.690474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2(:@0.332152:0.727124:0.345070:0.727124:0.345070:0.710735:0.332152:0.710735:0.000000:0.000000
1 1(:@0.370519:0.727124:0.406582:0.727124:0.406582:0.710735:0.370519:0.710735:0.000000:0.000000:0.000000:0.000000
0):@0.433449:0.727124:0.447841:0.727124:0.447841:0.710735:0.433449:0.710735:0.000000:0.000000
3(:@0.463762:0.727124:0.476680:0.727124:0.476680:0.710735:0.463762:0.710735:0.000000:0.000000
2):@0.502663:0.727124:0.516466:0.727124:0.516466:0.710735:0.502663:0.710735:0.000000:0.000000
02:@0.533751:0.727124:0.566570:0.727124:0.566570:0.710735:0.533751:0.710735:0.000000:0.000000
2:@0.592166:0.727124:0.601159:0.727124:0.601159:0.710735:0.592166:0.710735:0.000000
3:@0.643469:0.727124:0.652461:0.727124:0.652461:0.710735:0.643469:0.710735:0.000000
60 2:@0.677707:0.727124:0.737265:0.727124:0.737265:0.710735:0.677707:0.710735:0.000000:0.000000:0.000000:0.000000
3:@0.789674:0.727124:0.798666:0.727124:0.798666:0.710735:0.789674:0.710735:0.000000
80:@0.823654:0.727124:0.859404:0.727124:0.859404:0.710735:0.823654:0.710735:0.000000:0.000000
):@0.376895:0.727124:0.381778:0.727124:0.381778:0.710735:0.376895:0.710735:0.000000
;:@0.542946:0.727124:0.546152:0.727124:0.546152:0.710735:0.542946:0.710735:0.000000
,:@0.713660:0.727124:0.716866:0.727124:0.716866:0.710735:0.713660:0.710735:0.000000
x:@0.346839:0.727124:0.354302:0.727124:0.354302:0.710762:0.346839:0.710762:0.000000
y:@0.408609:0.727124:0.416090:0.727124:0.416090:0.710762:0.408609:0.710762:0.000000
z:@0.478136:0.727124:0.485378:0.727124:0.485378:0.710762:0.478136:0.710762:0.000000
x:@0.567344:0.727124:0.574807:0.727124:0.574807:0.710762:0.567344:0.710762:0.000000
y:@0.618333:0.727124:0.625815:0.727124:0.625815:0.710762:0.618333:0.710762:0.000000
z:@0.652941:0.727124:0.660183:0.727124:0.660183:0.710762:0.652941:0.710762:0.000000
x:@0.738058:0.727124:0.745521:0.727124:0.745521:0.710762:0.738058:0.710762:0.000000
y:@0.764557:0.727124:0.772038:0.727124:0.772038:0.710762:0.764557:0.710762:0.000000
z:@0.799145:0.727124:0.806388:0.727124:0.806388:0.710762:0.799145:0.710762:0.000000
−−:@0.358817:0.726709:0.394640:0.726709:0.394640:0.709767:0.358817:0.709767:0.000000:0.000000
−:@0.420587:0.726709:0.430703:0.726709:0.430703:0.709767:0.420587:0.709767:0.000000
+:@0.450587:0.726709:0.460703:0.726709:0.460703:0.709767:0.450587:0.709767:0.000000
−:@0.489801:0.726709:0.499917:0.726709:0.499917:0.709767:0.489801:0.709767:0.000000
=:@0.520059:0.726709:0.530176:0.726709:0.530176:0.709767:0.520059:0.709767:0.000000
−− +:@0.579322:0.726709:0.640428:0.726709:0.640428:0.709767:0.579322:0.709767:0.000000:0.000000:0.000000:0.000000
− =:@0.664605:0.726709:0.700889:0.726709:0.700889:0.709767:0.664605:0.709767:0.000000:0.000000:0.000000
− +:@0.750036:0.726709:0.786633:0.726709:0.786633:0.709767:0.750036:0.709767:0.000000:0.000000:0.000000
− =:@0.810810:0.726709:0.846836:0.726709:0.846836:0.709767:0.810810:0.709767:0.000000:0.000000:0.000000
  :@0.548843:0.727124:0.556914:0.727124:0.556914:0.710735:0.548843:0.710735:0.000000:0.000000
  :@0.719556:0.727124:0.727628:0.727124:0.727628:0.710735:0.719556:0.710735:0.000000:0.000000
Relación entre planos y vectores normales:@0.287495:0.759699:0.651977:0.759699:0.651977:0.741262:0.287495:0.741262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.287495:0.779545:0.303011:0.779545:0.303011:0.762410:0.287495:0.762410:0.000000:0.000000
Planos paralelos::@0.315985:0.779545:0.449051:0.779545:0.449051:0.762645:0.315985:0.762645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 dos planos son paralelos si sus vectores normales son paralelos :@0.449051:0.779545:0.907713:0.779545:0.907713:0.763157:0.449051:0.763157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre sí, es decir, uno es múltiplo del otro::@0.315985:0.796142:0.619630:0.796142:0.619630:0.779753:0.315985:0.779753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nn:@0.537208:0.816860:0.574414:0.816860:0.574414:0.800498:0.537208:0.800498:0.000000:0.000000
n:@0.627666:0.816857:0.637175:0.816857:0.637175:0.800496:0.627666:0.800496:0.000000
kn:@0.658551:0.816857:0.677014:0.816857:0.677014:0.800496:0.658551:0.800496:0.000000:0.000000
:@0.537935:0.805627:0.545491:0.805627:0.545491:0.788878:0.537935:0.788878:0.000000
:@0.565632:0.805627:0.573187:0.805627:0.573187:0.788878:0.565632:0.788878:0.000000
:@0.628249:0.805627:0.640209:0.805627:0.640209:0.788878:0.628249:0.788878:0.000000:0.000000
:@0.668237:0.805627:0.675793:0.805627:0.675793:0.788878:0.668237:0.788878:0.000000
1:@0.545841:0.816032:0.551053:0.816032:0.551053:0.806534:0.545841:0.806534:0.000000
2:@0.574217:0.816032:0.579428:0.816032:0.579428:0.806534:0.574217:0.806534:0.000000
1:@0.635466:0.818861:0.640678:0.818861:0.640678:0.809363:0.635466:0.809363:0.000000
2:@0.676823:0.816032:0.682034:0.816032:0.682034:0.806534:0.676823:0.806534:0.000000
||:@0.554111:0.816857:0.562054:0.816857:0.562054:0.800468:0.554111:0.800468:0.000000:0.000000
  :@0.581864:0.816857:0.589935:0.816857:0.589935:0.800468:0.581864:0.800468:0.000000:0.000000
  :@0.618719:0.816857:0.626790:0.816857:0.626790:0.800468:0.618719:0.800468:0.000000:0.000000
⇔:@0.594684:0.816442:0.613886:0.816442:0.613886:0.799500:0.594684:0.799500:0.000000
=:@0.644881:0.816442:0.654998:0.816442:0.654998:0.799500:0.644881:0.799500:0.000000
 :@0.287495:0.837285:0.291531:0.837285:0.291531:0.820896:0.287495:0.820896:0.000000
Por ejemplo: determinar si los planos 2:@0.315988:0.837285:0.601690:0.837027:0.601690:0.820638:0.315988:0.820896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.627304:0.837027:0.636297:0.837027:0.636297:0.820638:0.627304:0.820638:0.000000
40   y  4:@0.688963:0.837027:0.762766:0.837027:0.762766:0.820638:0.688963:0.820638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6:@0.787699:0.837027:0.796691:0.837027:0.796691:0.820638:0.787699:0.820638:0.000000
2:@0.823448:0.837027:0.832441:0.837027:0.832441:0.820638:0.823448:0.820638:0.000000
70:@0.857115:0.837027:0.892607:0.837027:0.892607:0.820638:0.857115:0.820638:0.000000:0.000000
x:@0.602482:0.837027:0.609946:0.837027:0.609946:0.820666:0.602482:0.820666:0.000000
y:@0.637347:0.837027:0.644829:0.837027:0.644829:0.820666:0.637347:0.820666:0.000000
z:@0.663570:0.837027:0.670812:0.837027:0.670812:0.820666:0.663570:0.820666:0.000000
x:@0.762619:0.837027:0.770082:0.837027:0.770082:0.820666:0.762619:0.820666:0.000000
y:@0.798313:0.837027:0.805794:0.837027:0.805794:0.820666:0.798313:0.820666:0.000000
z:@0.832920:0.837027:0.840162:0.837027:0.840162:0.820666:0.832920:0.820666:0.000000
−:@0.614460:0.836612:0.624577:0.836612:0.624577:0.819670:0.614460:0.819670:0.000000
+ +=:@0.649325:0.836612:0.712164:0.836612:0.712164:0.819670:0.649325:0.819670:0.000000:0.000000:0.000000:0.000000
−:@0.774596:0.836612:0.784713:0.836612:0.784713:0.819670:0.774596:0.819670:0.000000
+:@0.810309:0.836612:0.820426:0.836612:0.820426:0.819670:0.810309:0.819670:0.000000
−=:@0.844585:0.836612:0.880039:0.836612:0.880039:0.819670:0.844585:0.819670:0.000000:0.000000
son paralelos.:@0.315988:0.853881:0.415348:0.853881:0.415348:0.837492:0.315988:0.837492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.287499:0.874225:0.291534:0.874225:0.291534:0.857836:0.287499:0.857836:0.000000
Plano 1: 2:@0.315992:0.874225:0.386624:0.874141:0.386624:0.857752:0.315992:0.857836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.412239:0.874141:0.421231:0.874141:0.421231:0.857752:0.412239:0.857752:0.000000
40  vector normal :@0.473898:0.874141:0.625765:0.874141:0.625765:0.857752:0.473898:0.857752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
23 1,):@0.662154:0.874141:0.710348:0.874141:0.710348:0.857752:0.662154:0.857752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.634153:0.876145:0.639364:0.876145:0.639364:0.866647:0.634153:0.866647:0.000000
x:@0.387422:0.874141:0.394885:0.874141:0.394885:0.857780:0.387422:0.857780:0.000000
y:@0.422287:0.874141:0.429769:0.874141:0.429769:0.857780:0.422287:0.857780:0.000000
z:@0.448509:0.874141:0.455751:0.874141:0.455751:0.857780:0.448509:0.857780:0.000000
n:@0.626355:0.874141:0.635863:0.874141:0.635863:0.857780:0.626355:0.857780:0.000000
−:@0.399400:0.873726:0.409517:0.873726:0.409517:0.856784:0.399400:0.856784:0.000000
+ +=:@0.434265:0.873726:0.497103:0.873726:0.497103:0.856784:0.434265:0.856784:0.000000:0.000000:0.000000:0.000000
=:@0.643566:0.873726:0.653683:0.873726:0.653683:0.856784:0.643566:0.856784:0.000000
−:@0.676441:0.873726:0.686558:0.873726:0.686558:0.856784:0.676441:0.856784:0.000000
:@0.626926:0.862911:0.638885:0.862911:0.638885:0.846162:0.626926:0.846162:0.000000:0.000000
(,:@0.656926:0.874141:0.674008:0.874141:0.674008:0.857752:0.656926:0.857752:0.000000:0.000000
 :@0.287495:0.895034:0.291531:0.895034:0.291531:0.878645:0.287495:0.878645:0.000000
Plano 2: 4:@0.315988:0.895034:0.387078:0.894453:0.387078:0.878064:0.315988:0.878645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6:@0.413522:0.894453:0.422515:0.894453:0.422515:0.878064:0.413522:0.878064:0.000000
2:@0.449290:0.894453:0.458283:0.894453:0.458283:0.878064:0.449290:0.878064:0.000000
7 0  vector normal :@0.482957:0.894453:0.634540:0.894450:0.634540:0.878061:0.482957:0.878064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 62,):@0.673712:0.894450:0.726748:0.894450:0.726748:0.878061:0.673712:0.878061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.643606:0.896454:0.648818:0.896454:0.648818:0.886956:0.643606:0.886956:0.000000
x:@0.388447:0.894450:0.395910:0.894450:0.395910:0.878089:0.388447:0.878089:0.000000
y:@0.424160:0.894450:0.431641:0.894450:0.431641:0.878089:0.424160:0.878089:0.000000
z:@0.458754:0.894450:0.465996:0.894450:0.465996:0.878089:0.458754:0.878089:0.000000
n:@0.635124:0.894450:0.644633:0.894450:0.644633:0.878089:0.635124:0.878089:0.000000
−:@0.400430:0.894035:0.410547:0.894035:0.410547:0.877093:0.400430:0.877093:0.000000
+:@0.436143:0.894035:0.446260:0.894035:0.446260:0.877093:0.436143:0.877093:0.000000
−=:@0.470418:0.894035:0.505873:0.894035:0.505873:0.877093:0.470418:0.877093:0.000000:0.000000
=:@0.654529:0.894035:0.664645:0.894035:0.664645:0.877093:0.654529:0.877093:0.000000
−:@0.688565:0.894035:0.698681:0.894035:0.698681:0.877093:0.688565:0.877093:0.000000
:@0.635701:0.883220:0.649853:0.883220:0.649853:0.866471:0.635701:0.866471:0.000000:0.000000
:@0.640473:0.883220:0.648029:0.883220:0.648029:0.866471:0.640473:0.866471:0.000000
(,:@0.667897:0.894450:0.686122:0.894450:0.686122:0.878061:0.667897:0.878061:0.000000:0.000000
Como: (, 23 1:@0.315985:0.915709:0.421655:0.915194:0.421655:0.898805:0.315985:0.899320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,) 2 23:@0.408731:0.915197:0.491865:0.915194:0.491865:0.898805:0.408731:0.898808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.467146:0.915197:0.470353:0.915197:0.470353:0.898808:0.467146:0.898808:0.000000
, ,1  se comprueba que :@0.491489:0.915197:0.662652:0.915194:0.662652:0.898805:0.491489:0.898808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
||:@0.680435:0.915194:0.688377:0.915194:0.688377:0.898805:0.680435:0.898805:0.000000:0.000000
1:@0.672167:0.914369:0.677379:0.914369:0.677379:0.904871:0.672167:0.904871:0.000000
2:@0.700543:0.914369:0.705755:0.914369:0.705755:0.904871:0.700543:0.904871:0.000000
−:@0.390047:0.914779:0.400164:0.914779:0.400164:0.897837:0.390047:0.897837:0.000000
=:@0.427529:0.914779:0.437645:0.914779:0.437645:0.897837:0.427529:0.897837:0.000000
−:@0.472805:0.914779:0.482922:0.914779:0.482922:0.897837:0.472805:0.897837:0.000000
(:@0.451454:0.916529:0.457591:0.916529:0.457591:0.894877:0.451454:0.894877:0.000000
):@0.502444:0.916529:0.508580:0.916529:0.508580:0.894877:0.502444:0.894877:0.000000
nn:@0.663530:0.915194:0.700735:0.915194:0.700735:0.898833:0.663530:0.898833:0.000000:0.000000
:@0.664267:0.903964:0.644125:0.903964:0.644125:0.887215:0.664267:0.887215:0.000000
:@0.691964:0.903964:0.671822:0.903964:0.671822:0.887215:0.691964:0.887215:0.000000
, los planos son paralelos.:@0.708394:0.915709:0.892652:0.915709:0.892652:0.899320:0.708394:0.899320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nidad de conocimientos:@0.306727:0.416530:0.480398:0.416530:0.480398:0.401166:0.306727:0.401166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.417316:0.297460:0.417316:0.297460:0.400180:0.284892:0.400180:0.000000
Pienso y progreso:@0.294883:0.360610:0.417347:0.360610:0.417347:0.345246:0.294883:0.345246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Para qué sirven las torres de control aéreo?:@0.294883:0.378004:0.585350:0.378004:0.585350:0.363105:0.294883:0.363105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una torre de control aéreo está ubicada en el punto A(2, 0, 5), y necesita establecer :@0.287495:0.168345:0.907681:0.168345:0.907681:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una zona de vuelo segura para que los aviones se mantengan a una distancia ade-:@0.287495:0.184941:0.903587:0.184941:0.903587:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuada respecto de una montaña. La montaña tiene una superficie que puede mode-:@0.287495:0.201538:0.903666:0.201538:0.903666:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.741051:0.201538:0.745087:0.201538:0.745087:0.185149:0.741051:0.185149:0.000000
larse con un plano cuya ecuación es: 3  − 2  +   = 6:@0.287495:0.218134:0.665833:0.218134:0.665833:0.201745:0.287495:0.201745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.568498:0.218134:0.575962:0.218134:0.575962:0.201773:0.568498:0.201773:0.000000
y:@0.604009:0.218134:0.611490:0.218134:0.611490:0.201773:0.604009:0.201773:0.000000
z:@0.630544:0.218134:0.637786:0.218134:0.637786:0.201773:0.630544:0.201773:0.000000
a):@0.287495:0.241853:0.303011:0.241853:0.303011:0.224717:0.287495:0.224717:0.000000:0.000000
  ¿Cuál es el vector normal al plano que representa la montaña?:@0.303011:0.241853:0.771182:0.241853:0.771182:0.225464:0.303011:0.225464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.287495:0.262018:0.304154:0.262018:0.304154:0.244882:0.287495:0.244882:0.000000:0.000000
  La torre desea construir una ruta de vuelo recta desde el punto  (5, 1, 7).  Esa ruta :@0.304154:0.262018:0.907643:0.262018:0.907643:0.245629:0.304154:0.245629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.776843:0.262018:0.785615:0.262018:0.785615:0.245656:0.776843:0.245656:0.000000
será paralela al plano de la montaña para evitar colisiones. ¿Qué condición debe :@0.315985:0.278614:0.907731:0.278614:0.907731:0.262225:0.315985:0.262225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cumplir la dirección del vuelo respecto del vector normal del plano?:@0.315985:0.295211:0.814555:0.295211:0.814555:0.278822:0.315985:0.278822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c):@0.287495:0.315375:0.301593:0.315375:0.301593:0.298239:0.287495:0.298239:0.000000:0.000000
  Determina si el vector de dirección :@0.301593:0.315375:0.580709:0.315375:0.580709:0.298986:0.301593:0.298986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.581364:0.315272:0.589104:0.315272:0.589104:0.298911:0.581364:0.298911:0.000000
:@0.582359:0.304664:0.589915:0.304664:0.589915:0.287916:0.582359:0.287916:0.000000
=:@0.594448:0.314857:0.604565:0.314857:0.604565:0.297915:0.594448:0.297915:0.000000
−:@0.639467:0.314857:0.649583:0.314857:0.649583:0.297915:0.639467:0.297915:0.000000
(:@0.608116:0.316607:0.614253:0.316607:0.614253:0.294955:0.608116:0.294955:0.000000
):@0.656544:0.316607:0.662680:0.316607:0.662680:0.294955:0.656544:0.294955:0.000000
21 1  de una posible ruta de vuelo es :@0.615184:0.315272:0.907731:0.315371:0.907731:0.298982:0.615184:0.298883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,,:@0.623827:0.315272:0.637039:0.315272:0.637039:0.298883:0.623827:0.298883:0.000000:0.000000
paralelo al plano de la montaña. Justifica tu respuesta con el producto punto.:@0.315983:0.331968:0.881300:0.331968:0.881300:0.315579:0.315983:0.315579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.592023:0.331968:0.596059:0.331968:0.596059:0.315579:0.592023:0.315579:0.000000
Ecuación del plano :@0.286308:0.075160:0.570646:0.075160:0.570646:0.041608:0.286308:0.041608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108603:0.183816:0.108603:0.183816:0.011514:0.094760:0.011514:0.000000:0.000000
¿Qué entiendes por :@0.112709:0.191813:0.247834:0.191813:0.247834:0.176914:0.112709:0.176914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores ortogonales?:@0.096945:0.205643:0.244164:0.205643:0.244164:0.190744:0.096945:0.190744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.162936:0.227756:0.162936:0.227756:0.146036:0.108521:0.146036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.068421:0.282312:0.068421:0.239486:0.056510:0.239486:0.056510:0.282312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En navegación aérea se :@0.074990:0.401601:0.218719:0.401601:0.218719:0.388192:0.074990:0.388192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emplean vectores.:@0.074990:0.414173:0.184886:0.414173:0.184886:0.400763:0.074990:0.400763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vector normal del plano:@0.079491:0.496089:0.253280:0.496089:0.253280:0.480725:0.079491:0.480725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vectores paralelos:@0.100230:0.686319:0.232539:0.686319:0.232539:0.670955:0.100230:0.670955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vectores perpendiculares:@0.074515:0.728640:0.258269:0.728640:0.258269:0.713276:0.074515:0.713276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.031312:0.513845:0.039405:0.513845:0.039405:0.499095:0.031312:0.499095:0.000000
60 2:@0.062127:0.513845:0.115729:0.513845:0.115729:0.499095:0.062127:0.499095:0.000000:0.000000:0.000000:0.000000
3:@0.162896:0.513845:0.170990:0.513845:0.170990:0.499095:0.162896:0.499095:0.000000
80:@0.193479:0.513845:0.225654:0.513845:0.225654:0.499095:0.193479:0.499095:0.000000:0.000000
,:@0.094484:0.513845:0.097370:0.513845:0.097370:0.499095:0.094484:0.499095:0.000000
y:@0.008690:0.513845:0.015424:0.513845:0.015424:0.499120:0.008690:0.499120:0.000000
z:@0.039837:0.513845:0.046355:0.513845:0.046355:0.499120:0.039837:0.499120:0.000000
x:@0.116442:0.513845:0.123159:0.513845:0.123159:0.499120:0.116442:0.499120:0.000000
y:@0.140291:0.513845:0.147025:0.513845:0.147025:0.499120:0.140291:0.499120:0.000000
z:@0.171421:0.513845:0.177939:0.513845:0.177939:0.499120:0.171421:0.499120:0.000000
−− +:@-0.026420:0.513472:0.028576:0.513472:0.028576:0.498224:-0.026420:0.498224:0.000000:0.000000:0.000000:0.000000
− =:@0.050335:0.513472:0.082991:0.513472:0.082991:0.498224:0.050335:0.498224:0.000000:0.000000:0.000000
− +:@0.127222:0.513472:0.160160:0.513472:0.160160:0.498224:0.127222:0.498224:0.000000:0.000000:0.000000
− =:@0.181919:0.513472:0.214343:0.513472:0.214343:0.498224:0.181919:0.498224:0.000000:0.000000:0.000000
  :@0.099791:0.513845:0.107055:0.513845:0.107055:0.499095:0.099791:0.499095:0.000000:0.000000
z:@0.166672:0.541899:0.173256:0.541899:0.173256:0.527025:0.166672:0.527025:0.000000
x:@0.094151:0.652378:0.100936:0.652378:0.100936:0.637504:0.094151:0.637504:0.000000
y:@0.242544:0.639906:0.249345:0.639906:0.249345:0.625032:0.242544:0.625032:0.000000
n:@0.050269:0.748856:0.058827:0.748856:0.058827:0.734131:0.050269:0.734131:0.000000
n:@0.080902:0.748856:0.089459:0.748856:0.089459:0.734131:0.080902:0.734131:0.000000
nn:@0.137387:0.748856:0.165963:0.748856:0.165963:0.734131:0.137387:0.734131:0.000000:0.000000
:@0.050929:0.738748:0.057729:0.738748:0.057729:0.723675:0.050929:0.723675:0.000000
:@0.081561:0.738748:0.088361:0.738748:0.088361:0.723675:0.081561:0.723675:0.000000
 :@0.137900:0.738748:0.164867:0.738748:0.164867:0.723675:0.137900:0.723675:0.000000:0.000000:0.000000:0.000000
1:@0.058043:0.748113:0.062734:0.748113:0.062734:0.739565:0.058043:0.739565:0.000000
2:@0.089281:0.748113:0.093972:0.748113:0.093972:0.739565:0.089281:0.739565:0.000000
1:@0.144404:0.750660:0.149095:0.750660:0.149095:0.742112:0.144404:0.742112:0.000000
2:@0.165798:0.748113:0.170488:0.748113:0.170488:0.739565:0.165798:0.739565:0.000000
0:@0.187943:0.748856:0.196036:0.748856:0.196036:0.734106:0.187943:0.734106:0.000000
⊥:@0.066524:0.748483:0.077437:0.748483:0.077437:0.733235:0.066524:0.733235:0.000000
⇔:@0.107705:0.748483:0.124986:0.748483:0.124986:0.733235:0.107705:0.733235:0.000000
⋅:@0.151339:0.748483:0.155486:0.748483:0.155486:0.733235:0.151339:0.733235:0.000000
=:@0.175653:0.748483:0.184758:0.748483:0.184758:0.733235:0.175653:0.733235:0.000000
  :@0.096161:0.748856:0.103426:0.748856:0.103426:0.734106:0.096161:0.734106:0.000000:0.000000
  :@0.129331:0.748856:0.136595:0.748856:0.136595:0.734106:0.129331:0.734106:0.000000:0.000000
nn:@0.101034:0.704082:0.134519:0.704082:0.134519:0.689357:0.101034:0.689357:0.000000:0.000000
n:@0.182449:0.704082:0.191007:0.704082:0.191007:0.689357:0.182449:0.689357:0.000000
kn:@0.210245:0.704082:0.226863:0.704082:0.226863:0.689357:0.210245:0.689357:0.000000:0.000000
:@0.101697:0.693975:0.108497:0.693975:0.108497:0.678901:0.101697:0.678901:0.000000
:@0.126624:0.693975:0.133424:0.693975:0.133424:0.678901:0.126624:0.678901:0.000000
:@0.182980:0.693975:0.193743:0.693975:0.193743:0.678901:0.182980:0.678901:0.000000:0.000000
:@0.218969:0.693975:0.225769:0.693975:0.225769:0.678901:0.218969:0.678901:0.000000
1:@0.108808:0.703341:0.113498:0.703341:0.113498:0.694793:0.108808:0.694793:0.000000
2:@0.134346:0.703341:0.139037:0.703341:0.139037:0.694793:0.134346:0.694793:0.000000
1:@0.189470:0.705887:0.194161:0.705887:0.194161:0.697339:0.189470:0.697339:0.000000
2:@0.226693:0.703341:0.231383:0.703341:0.231383:0.694793:0.226693:0.694793:0.000000
||:@0.116252:0.704082:0.123401:0.704082:0.123401:0.689332:0.116252:0.689332:0.000000:0.000000
  :@0.141229:0.704082:0.148493:0.704082:0.148493:0.689332:0.141229:0.689332:0.000000:0.000000
  :@0.174399:0.704082:0.181663:0.704082:0.181663:0.689332:0.174399:0.689332:0.000000:0.000000
⇔:@0.152772:0.703709:0.170054:0.703709:0.170054:0.688461:0.152772:0.688461:0.000000
=:@0.197950:0.703709:0.207055:0.703709:0.207055:0.688461:0.197950:0.688461:0.000000
z:@0.135968:0.770767:0.142552:0.770767:0.142552:0.755893:0.135968:0.755893:0.000000
Plano 2:@0.189593:0.806625:0.238761:0.806625:0.238761:0.791726:0.189593:0.791726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.063447:0.914275:0.070232:0.914275:0.070232:0.899401:0.063447:0.899401:0.000000
y:@0.216430:0.893027:0.223232:0.893027:0.223232:0.878153:0.216430:0.878153:0.000000
n:@0.183222:0.571568:0.190829:0.571568:0.190829:0.558479:0.183222:0.558479:0.000000
:@0.183808:0.562584:0.189852:0.562584:0.189852:0.549185:0.183808:0.549185:0.000000
=:@0.193692:0.571236:0.201785:0.571236:0.201785:0.557682:0.193692:0.557682:0.000000
−:@0.219992:0.571236:0.228085:0.571236:0.228085:0.557682:0.219992:0.557682:0.000000
(,21:@0.204365:0.571568:0.235228:0.571568:0.235228:0.558457:0.204365:0.558457:0.000000:0.000000:0.000000:0.000000
,):@0.232893:0.571568:0.248018:0.571568:0.248018:0.558457:0.232893:0.558457:0.000000:0.000000
3:@0.236953:0.571568:0.244147:0.571568:0.244147:0.558457:0.236953:0.558457:0.000000
n:@0.083635:0.823757:0.092193:0.823757:0.092193:0.809032:0.083635:0.809032:0.000000
n:@0.114267:0.823757:0.122825:0.823757:0.122825:0.809032:0.114267:0.809032:0.000000
nn:@0.170755:0.823757:0.199331:0.823757:0.199331:0.809032:0.170755:0.809032:0.000000:0.000000
:@0.084298:0.813650:0.091098:0.813650:0.091098:0.798576:0.084298:0.798576:0.000000
:@0.114930:0.813650:0.121730:0.813650:0.121730:0.798576:0.114930:0.798576:0.000000
 :@0.171269:0.813650:0.198236:0.813650:0.198236:0.798576:0.171269:0.798576:0.000000:0.000000:0.000000:0.000000
1:@0.091409:0.823015:0.096099:0.823015:0.096099:0.814466:0.091409:0.814466:0.000000
2:@0.122647:0.823015:0.127337:0.823015:0.127337:0.814466:0.122647:0.814466:0.000000
1:@0.177772:0.825561:0.182463:0.825561:0.182463:0.817012:0.177772:0.817012:0.000000
2:@0.199163:0.823015:0.203854:0.823015:0.203854:0.814466:0.199163:0.814466:0.000000
0:@0.221308:0.823757:0.229402:0.823757:0.229402:0.809007:0.221308:0.809007:0.000000
⊥:@0.099891:0.823384:0.110803:0.823384:0.110803:0.808136:0.099891:0.808136:0.000000
⇔:@0.141071:0.823384:0.158352:0.823384:0.158352:0.808136:0.141071:0.808136:0.000000
⋅:@0.184706:0.823384:0.188852:0.823384:0.188852:0.808136:0.184706:0.808136:0.000000
=:@0.209019:0.823384:0.218124:0.823384:0.218124:0.808136:0.209019:0.808136:0.000000
  :@0.129528:0.823757:0.136792:0.823757:0.136792:0.809007:0.129528:0.809007:0.000000:0.000000
  :@0.162697:0.823757:0.169962:0.823757:0.169962:0.809007:0.162697:0.809007:0.000000:0.000000
n:@0.094770:0.873778:0.103327:0.873778:0.103327:0.859053:0.094770:0.859053:0.000000
n:@0.125402:0.873778:0.133960:0.873778:0.133960:0.859053:0.125402:0.859053:0.000000
nn:@0.181890:0.873778:0.210466:0.873778:0.210466:0.859053:0.181890:0.859053:0.000000:0.000000
:@0.095433:0.863670:0.102233:0.863670:0.102233:0.848597:0.095433:0.848597:0.000000
:@0.126065:0.863670:0.132865:0.863670:0.132865:0.848597:0.126065:0.848597:0.000000
 :@0.182404:0.863670:0.209371:0.863670:0.209371:0.848597:0.182404:0.848597:0.000000:0.000000:0.000000:0.000000
1:@0.102544:0.873035:0.107234:0.873035:0.107234:0.864487:0.102544:0.864487:0.000000
2:@0.133782:0.873035:0.138472:0.873035:0.138472:0.864487:0.133782:0.864487:0.000000
1:@0.188908:0.875581:0.193598:0.875581:0.193598:0.867033:0.188908:0.867033:0.000000
2:@0.210299:0.873035:0.214989:0.873035:0.214989:0.864487:0.210299:0.864487:0.000000
0:@0.232444:0.873778:0.240537:0.873778:0.240537:0.859028:0.232444:0.859028:0.000000
⊥:@0.111026:0.873404:0.121939:0.873404:0.121939:0.858156:0.111026:0.858156:0.000000
⇔:@0.152206:0.873404:0.169488:0.873404:0.169488:0.858156:0.152206:0.858156:0.000000
⋅:@0.195841:0.873404:0.199987:0.873404:0.199987:0.858156:0.195841:0.858156:0.000000
=:@0.220154:0.873404:0.229259:0.873404:0.229259:0.858156:0.220154:0.858156:0.000000
  :@0.140663:0.873778:0.147927:0.873778:0.147927:0.859028:0.140663:0.859028:0.000000:0.000000
  :@0.173833:0.873778:0.181097:0.873778:0.181097:0.859028:0.173833:0.859028:0.000000:0.000000
M.5.2.23.:@0.298180:0.946788:0.353208:0.946788:0.353208:0.934325:0.298180:0.934325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  Determinar si dos planos son paralelos (cuando no hay solución) o perpendiculares (si los vectores :@0.353207:0.946788:0.906571:0.946788:0.906571:0.934868:0.353207:0.934868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
normales a los planos son perpendiculares) para resolver aplicaciones geométricas en  .:@0.298180:0.958103:0.772630:0.958103:0.772630:0.946184:0.298180:0.946184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.766485:0.953705:0.770298:0.953705:0.770298:0.946756:0.766485:0.946756:0.000000