204:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
El conjunto :@0.404235:0.134794:0.551438:0.134794:0.551438:0.090135:0.404235:0.090135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.551438:0.132795:0.587724:0.132795:0.587724:0.097716:0.551438:0.097716:0.000000
3:@0.587708:0.115928:0.595912:0.115928:0.595912:0.089892:0.587708:0.089892:0.000000
M.5.2.18. Realizar las operaciones de adición entre elementos de :@0.143726:0.938561:0.422963:0.938561:0.422963:0.928519:0.143726:0.928519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.423209:0.937972:0.431676:0.937972:0.431676:0.929787:0.423209:0.929787:0.000000
3:@0.431700:0.934695:0.434715:0.934695:0.434715:0.928840:0.431700:0.928840:0.000000
 y de producto por un número escalar de manera geométrica y analítica, aplicando propiedades de los :@0.434715:0.938561:0.883198:0.938561:0.883198:0.928519:0.434715:0.928519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números reales; y reconocer los vectores como elementos geométricos de  .:@0.143730:0.949123:0.477967:0.949123:0.477967:0.939080:0.143730:0.939080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.464813:0.948533:0.473280:0.948533:0.473280:0.940348:0.464813:0.940348:0.000000
3:@0.473276:0.945256:0.476291:0.945256:0.476291:0.939401:0.473276:0.939401:0.000000
Los elementos del espacio vectorial   se identifican con los vectores :@0.404236:0.160347:0.895930:0.160347:0.895930:0.143849:0.404236:0.143849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.657283:0.159260:0.670588:0.159260:0.670588:0.146398:0.657283:0.146398:0.000000
3:@0.670588:0.153995:0.675541:0.153995:0.675541:0.144377:0.670588:0.144377:0.000000
en el plano. Las ecuaciones vectoriales recta y de planos, así como sus :@0.404227:0.177697:0.895982:0.177697:0.895982:0.161200:0.404227:0.161200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representaciones gráficas, constituyen otros elementos importantes :@0.404227:0.195048:0.895913:0.195048:0.895913:0.178551:0.404227:0.178551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en las aplicaciones.:@0.404227:0.212399:0.537598:0.212399:0.537598:0.195901:0.404227:0.195901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se designa con   al producto cartesiano   ×   ×  , esto es,:@0.404227:0.247101:0.836628:0.247101:0.836628:0.230603:0.404227:0.230603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.513448:0.246014:0.526753:0.246014:0.526753:0.233151:0.513448:0.233151:0.000000
3:@0.526753:0.240749:0.531706:0.240749:0.531706:0.231131:0.526753:0.231131:0.000000
R:@0.700410:0.246014:0.713715:0.246014:0.713715:0.233151:0.700410:0.233151:0.000000
R:@0.732806:0.246014:0.746111:0.246014:0.746111:0.233151:0.732806:0.233151:0.000000
R:@0.765202:0.246014:0.778507:0.246014:0.778507:0.233151:0.765202:0.233151:0.000000
R:@0.404236:0.263364:0.417541:0.263364:0.417541:0.250502:0.404236:0.250502:0.000000
3:@0.417541:0.258100:0.422494:0.258100:0.422494:0.248481:0.417541:0.248481:0.000000
 = {( ,  ,  ) |  ,  ,      }. Los elementos de   son ternas ordenadas.:@0.422493:0.264451:0.891774:0.264451:0.891774:0.247954:0.422493:0.247954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z x y z:@0.452720:0.264567:0.541109:0.264567:0.541109:0.248098:0.452720:0.248098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.544948:0.263933:0.559600:0.263933:0.559600:0.250559:0.544948:0.250559:0.000000
R:@0.563404:0.263364:0.576709:0.263364:0.576709:0.250502:0.563404:0.250502:0.000000
R:@0.715916:0.263364:0.729221:0.263364:0.729221:0.250502:0.715916:0.250502:0.000000
3:@0.729221:0.258100:0.734174:0.258100:0.734174:0.248481:0.729221:0.248481:0.000000
Si ( ,  ,  )    ,       se denomina primera componente o abscisa, :@0.404238:0.281802:0.895903:0.281802:0.895903:0.265304:0.404238:0.265304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.426778:0.281918:0.463652:0.281918:0.463652:0.265449:0.426778:0.265449:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.474387:0.281283:0.489039:0.281283:0.489039:0.267910:0.474387:0.267910:0.000000
R:@0.493818:0.280715:0.507123:0.280715:0.507123:0.267853:0.493818:0.267853:0.000000
3:@0.507123:0.275450:0.512076:0.275450:0.512076:0.265832:0.507123:0.265832:0.000000
x:@0.519609:0.281918:0.527084:0.281918:0.527084:0.265449:0.519609:0.265449:0.000000
:@0.531864:0.281283:0.546517:0.281283:0.546517:0.267910:0.531864:0.267910:0.000000
R:@0.551297:0.280715:0.564602:0.280715:0.564602:0.267853:0.551297:0.267853:0.000000
y:@0.404236:0.299268:0.411923:0.299268:0.411923:0.282800:0.404236:0.282800:0.000000
     se denomina segunda componente u ordenada,   se llama :@0.411923:0.299153:0.895906:0.299153:0.895906:0.282655:0.411923:0.282655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.418474:0.298634:0.433127:0.298634:0.433127:0.285261:0.418474:0.285261:0.000000
R:@0.439678:0.298066:0.452982:0.298066:0.452982:0.285204:0.439678:0.285204:0.000000
z:@0.819440:0.299268:0.826087:0.299268:0.826087:0.282800:0.819440:0.282800:0.000000
tercera componente. A los elementos de :@0.404241:0.316504:0.703612:0.316504:0.703612:0.300006:0.404241:0.300006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.704970:0.315417:0.718275:0.315417:0.718275:0.302554:0.704970:0.302554:0.000000
3:@0.718275:0.310151:0.723228:0.310151:0.723228:0.300532:0.718275:0.300532:0.000000
 los representamos con :@0.723227:0.316504:0.895919:0.316504:0.895919:0.300006:0.723227:0.300006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las letras mayúsculas del alfabeto y a sus componentes, siempre con :@0.404233:0.333854:0.895992:0.333854:0.895992:0.317357:0.404233:0.317357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
letras minúsculas del alfabeto, con o sin subíndices. Así, escribiremos :@0.404233:0.351205:0.895955:0.351205:0.895955:0.334707:0.404233:0.334707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.404233:0.368671:0.416177:0.368671:0.416177:0.352203:0.404233:0.352203:0.000000
 = ( ,  ,  )    . También escribiremos      . En este último caso, :@0.416177:0.368556:0.895919:0.368556:0.895919:0.352058:0.416177:0.352058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.441338:0.368671:0.477055:0.368671:0.477055:0.352203:0.441338:0.352203:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.487206:0.368037:0.501858:0.368037:0.501858:0.354664:0.487206:0.354664:0.000000
R:@0.506056:0.367469:0.519360:0.367469:0.519360:0.354607:0.506056:0.354607:0.000000
3:@0.519360:0.362204:0.524314:0.362204:0.524314:0.352586:0.519360:0.352586:0.000000
A:@0.691265:0.368671:0.702535:0.368671:0.702535:0.352203:0.691265:0.352203:0.000000
:@0.706729:0.368037:0.721382:0.368037:0.721382:0.354664:0.706729:0.354664:0.000000
R:@0.725581:0.367469:0.738885:0.367469:0.738885:0.354607:0.725581:0.354607:0.000000
3:@0.738885:0.362204:0.743839:0.362204:0.743839:0.352586:0.738885:0.352586:0.000000
quedará sobreentendido que   es una terna ordenada, esto es, que :@0.404231:0.385907:0.895881:0.385907:0.895881:0.369409:0.404231:0.369409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.619000:0.386022:0.630270:0.386022:0.630270:0.369553:0.619000:0.369553:0.000000
existen  ,  ,      , tal que   = ( ,  ,  ). Se tiene, entonces, la siguiente :@0.404231:0.403257:0.895920:0.403257:0.895920:0.386760:0.404231:0.386760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.457384:0.403373:0.496107:0.403373:0.496107:0.386904:0.457384:0.386904:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.500023:0.402739:0.514676:0.402739:0.514676:0.389365:0.500023:0.389365:0.000000
R :@0.518578:0.402170:0.539244:0.402170:0.539244:0.389308:0.518578:0.389308:0.000000:0.000000
A:@0.591782:0.403373:0.603052:0.403373:0.603052:0.386904:0.591782:0.386904:0.000000
a b c:@0.627615:0.403373:0.666358:0.403373:0.666358:0.386904:0.627615:0.386904:0.000000:0.000000:0.000000:0.000000:0.000000
equivalencia:  :@0.404235:0.420608:0.503142:0.420608:0.503142:0.404110:0.404235:0.404110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.492065:0.445203:0.503335:0.445203:0.503335:0.428734:0.492065:0.428734:0.000000
     :@0.503335:0.445087:0.548666:0.445086:0.548666:0.428589:0.503335:0.428589:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.507473:0.444568:0.522125:0.444568:0.522125:0.431195:0.507473:0.431195:0.000000
R:@0.526267:0.443999:0.539572:0.443999:0.539572:0.431137:0.526267:0.431137:0.000000
3:@0.539570:0.438735:0.544524:0.438735:0.544524:0.429117:0.539570:0.429117:0.000000
⇔:@0.548666:0.444580:0.568741:0.444580:0.568741:0.426868:0.548666:0.426868:0.000000
 :@0.568741:0.445086:0.572883:0.445086:0.572883:0.428589:0.568741:0.428589:0.000000
∃:@0.572883:0.452161:0.583208:0.452161:0.583208:0.434025:0.572883:0.434025:0.000000
a, b, c :@0.583205:0.445202:0.626032:0.445202:0.626032:0.428733:0.583205:0.428733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.626033:0.444568:0.640685:0.444568:0.640685:0.431195:0.626033:0.431195:0.000000
    tal que   = ( , , ).:@0.640685:0.445086:0.803949:0.445086:0.803949:0.428589:0.640685:0.428589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.644826:0.443999:0.658130:0.443999:0.658130:0.431137:0.644826:0.431137:0.000000
A:@0.719702:0.445202:0.730972:0.445202:0.730972:0.428733:0.719702:0.428733:0.000000
a b c:@0.756017:0.445202:0.795241:0.445202:0.795241:0.428733:0.756017:0.428733:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.404234:0.480164:0.522212:0.480164:0.522212:0.463377:0.404234:0.463377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los siguientes son elementos de  :    = (0, 1, 5),     =  –8, –     ,    2  ,:@0.404234:0.497139:0.887437:0.497139:0.887437:0.480641:0.404234:0.480641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.635339:0.496052:0.648644:0.496052:0.648644:0.483190:0.635339:0.483190:0.000000
3:@0.648644:0.490787:0.653597:0.490787:0.653597:0.481169:0.648644:0.481169:0.000000
A:@0.664635:0.497254:0.675905:0.497254:0.675905:0.480786:0.664635:0.480786:0.000000
   :@0.712201:0.497254:0.731735:0.497254:0.731735:0.480786:0.712201:0.480786:0.000000:0.000000:0.000000
B:@0.761365:0.497254:0.770555:0.497254:0.770555:0.480786:0.761365:0.480786:0.000000
C:@0.404226:0.525290:0.414263:0.525290:0.414263:0.508822:0.404226:0.508822:0.000000
 = (0, 0, –3),    = (2, 0, 0),    = (0, 1, 0),    = (–    2 , –    2,    2 ),:@0.414263:0.525175:0.852723:0.525175:0.852723:0.508677:0.414263:0.508677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.450559:0.525290:0.470094:0.525290:0.470094:0.508822:0.450559:0.508822:0.000000:0.000000:0.000000
D:@0.506082:0.525290:0.517718:0.525290:0.517718:0.508822:0.506082:0.508822:0.000000
   :@0.554013:0.525290:0.573548:0.525290:0.573548:0.508822:0.554013:0.508822:0.000000:0.000000:0.000000
M:@0.599036:0.525290:0.614314:0.525290:0.614314:0.508822:0.599036:0.508822:0.000000
   :@0.650609:0.525290:0.670144:0.525290:0.670144:0.508822:0.650609:0.508822:0.000000:0.000000:0.000000
N:@0.695632:0.525290:0.707538:0.525290:0.707538:0.508822:0.695632:0.508822:0.000000
0 = (0, 0, 0). El elemento 0 = (0, 0, 0) se llama elemento nulo de  .:@0.404226:0.549654:0.873043:0.549661:0.873043:0.533164:0.404226:0.533156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.852031:0.548574:0.865336:0.548574:0.865336:0.535712:0.852031:0.535712:0.000000
3:@0.865334:0.543308:0.870287:0.543308:0.870287:0.533690:0.865334:0.533690:0.000000
Igualdad de elementos de :@0.404236:0.585760:0.613302:0.585760:0.613302:0.568078:0.404236:0.568078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.613302:0.584267:0.627816:0.584267:0.627816:0.570235:0.613302:0.570235:0.000000
3:@0.627815:0.578930:0.633523:0.578930:0.633523:0.568621:0.627815:0.568621:0.000000
Definición :@0.404236:0.602931:0.491103:0.602931:0.491103:0.585985:0.404236:0.585985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean   = ( ,  ,  ),   = ( ,  ,  )    . Diremos que   es :@0.484322:0.602468:0.870701:0.602468:0.870701:0.585970:0.484322:0.585970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.528902:0.602584:0.540172:0.602584:0.540172:0.586115:0.528902:0.586115:0.000000
a b c B:@0.565217:0.602584:0.626480:0.602584:0.626480:0.586115:0.565217:0.586115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.651525:0.602584:0.687127:0.602584:0.687127:0.586115:0.651525:0.586115:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.697216:0.601949:0.711868:0.601949:0.711868:0.588576:0.697216:0.588576:0.000000
R:@0.716010:0.601381:0.729315:0.601381:0.729315:0.588519:0.716010:0.588519:0.000000
3:@0.729313:0.596115:0.734266:0.596115:0.734266:0.586497:0.729313:0.586497:0.000000
A:@0.836775:0.602584:0.848045:0.602584:0.848045:0.586115:0.836775:0.586115:0.000000
igual a  , que se escribe   =   si y solo si   =  ,   =  ,   =  . :@0.404234:0.619819:0.816429:0.619819:0.816429:0.603321:0.404234:0.603321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.453456:0.619934:0.462646:0.619934:0.462646:0.603465:0.453456:0.603465:0.000000
A B:@0.573456:0.619934:0.613007:0.619934:0.613007:0.603465:0.573456:0.603465:0.000000:0.000000:0.000000
a x b y c z:@0.691224:0.619934:0.809532:0.619934:0.809532:0.603465:0.691224:0.603465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la definición de igualdad de ternas ordenadas, tenemos la siguien-:@0.404234:0.654520:0.891793:0.654520:0.891793:0.638022:0.404234:0.638022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
te equivalencia: :@0.404234:0.671871:0.517203:0.671871:0.517203:0.655373:0.404234:0.655373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.536798:0.689337:0.576349:0.689337:0.576349:0.672869:0.536798:0.672869:0.000000:0.000000:0.000000
 =   :@0.548068:0.689222:0.580491:0.689222:0.580491:0.672724:0.548068:0.672724:0.000000:0.000000:0.000000:0.000000:0.000000
⇔:@0.580491:0.688716:0.600566:0.688716:0.600566:0.671003:0.580491:0.671003:0.000000
 (  = :@0.600566:0.689222:0.638730:0.689222:0.638730:0.672724:0.600566:0.672724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a x  b y  c z:@0.610661:0.689337:0.750508:0.689337:0.750508:0.672869:0.610661:0.672869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∧:@0.650339:0.695271:0.659729:0.695271:0.659729:0.678862:0.650339:0.678862:0.000000
   = :@0.659727:0.689222:0.692227:0.689222:0.692227:0.672724:0.659727:0.672724:0.000000:0.000000:0.000000:0.000000:0.000000
∧:@0.704054:0.695271:0.713444:0.695271:0.713444:0.678862:0.704054:0.678862:0.000000
   =  ),:@0.713442:0.689222:0.759216:0.689222:0.759216:0.672724:0.713442:0.672724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donde   denota el conectivo lógico conjunción. La definición expresa :@0.404235:0.723923:0.895955:0.723923:0.895955:0.707425:0.404235:0.707425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∧:@0.454455:0.729972:0.463845:0.729972:0.463845:0.713564:0.454455:0.713564:0.000000
que dos elementos de   son iguales si y solo si sus respectivos com-:@0.404235:0.741274:0.891704:0.741274:0.891704:0.724776:0.404235:0.724776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.565379:0.740187:0.578684:0.740187:0.578684:0.727325:0.565379:0.727325:0.000000
3:@0.578684:0.734921:0.583637:0.734921:0.583637:0.725303:0.578684:0.725303:0.000000
ponentes son iguales. De la definición de igualdad se desprende in-:@0.404240:0.758625:0.891703:0.758625:0.891703:0.742127:0.404240:0.742127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mediatamente su negación: si   = ( ,  ,  ),   = ( ,  ,  )    ,entonces, :@0.404240:0.775975:0.895912:0.775975:0.895912:0.759478:0.404240:0.759478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.617639:0.776091:0.628909:0.776091:0.628909:0.759622:0.617639:0.759622:0.000000
a b c B:@0.653222:0.776091:0.713447:0.776091:0.713447:0.759622:0.653222:0.759622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.737760:0.776091:0.772649:0.776091:0.772649:0.759622:0.737760:0.759622:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.782400:0.775457:0.797052:0.775457:0.797052:0.762083:0.782400:0.762083:0.000000
R:@0.800836:0.774888:0.814141:0.774888:0.814141:0.762026:0.800836:0.762026:0.000000
3  :@0.814141:0.769622:0.824263:0.769622:0.824263:0.760004:0.814141:0.760004:0.000000:0.000000:0.000000
A:@0.404245:0.793442:0.415516:0.793442:0.415516:0.776973:0.404245:0.776973:0.000000
 ≠   :@0.415516:0.793326:0.448671:0.793326:0.448671:0.776828:0.415516:0.776828:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.435340:0.793442:0.444529:0.793442:0.444529:0.776973:0.435340:0.776973:0.000000
⇔:@0.449056:0.792820:0.469131:0.792820:0.469131:0.775108:0.449056:0.775108:0.000000
 (  ≠ :@0.469131:0.793326:0.508027:0.793326:0.508027:0.776828:0.469131:0.776828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.479592:0.793442:0.488569:0.793442:0.488569:0.776973:0.479592:0.776973:0.000000
x  b:@0.508393:0.793442:0.543562:0.793442:0.543562:0.776973:0.508393:0.776973:0.000000:0.000000:0.000000:0.000000
∨:@0.520401:0.799375:0.529790:0.799375:0.529790:0.782967:0.520401:0.782967:0.000000
   ≠ :@0.529787:0.793326:0.563020:0.793326:0.563020:0.776828:0.529787:0.776828:0.000000:0.000000:0.000000:0.000000:0.000000
y  c:@0.563386:0.793442:0.596692:0.793442:0.596692:0.776973:0.563386:0.776973:0.000000:0.000000:0.000000:0.000000
∨:@0.575612:0.799375:0.585001:0.799375:0.585001:0.782967:0.575612:0.782967:0.000000
   ≠  ), donde   denota el conectivo lógico :@0.584998:0.793326:0.895881:0.793326:0.895881:0.776828:0.584998:0.776828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.616516:0.793442:0.623162:0.793442:0.623162:0.776973:0.616516:0.776973:0.000000
∨:@0.687814:0.799375:0.697204:0.799375:0.697204:0.782967:0.687814:0.782967:0.000000
disyunción.:@0.404235:0.810677:0.484302:0.810677:0.484302:0.794179:0.404235:0.794179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sistemas de coordenadas espaciales:@0.404236:0.846776:0.689188:0.846776:0.689188:0.829093:0.404236:0.829093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Primeramente establecemos una correspondencia biunívoca (biyec-:@0.404236:0.863484:0.891763:0.863484:0.891763:0.846986:0.404236:0.846986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción) entre los puntos del espacio y las ternas ordenadas ( ,  ,  )    . :@0.404236:0.880834:0.895912:0.880834:0.895912:0.864337:0.404236:0.864337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.805769:0.880950:0.843426:0.880950:0.843426:0.864481:0.805769:0.864481:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.852745:0.880316:0.867397:0.880316:0.867397:0.866942:0.852745:0.866942:0.000000
R:@0.870759:0.879747:0.884063:0.879747:0.884063:0.866885:0.870759:0.866885:0.000000
3:@0.884063:0.874481:0.889017:0.874481:0.889017:0.864863:0.884063:0.864863:0.000000
Denotamos con   el conjunto de puntos del espacio.:@0.404244:0.898185:0.784336:0.898185:0.784336:0.881687:0.404244:0.881687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.523879:0.898301:0.531836:0.898301:0.531836:0.881832:0.523879:0.881832:0.000000
3:@0.531827:0.901462:0.536781:0.901462:0.536781:0.891844:0.531827:0.891844:0.000000
5:@0.747367:0.516453:0.752320:0.516453:0.752320:0.506835:0.747367:0.506835:0.000000
4:@0.792372:0.516453:0.797325:0.516453:0.797325:0.506835:0.792372:0.506835:0.000000
5:@0.835311:0.489849:0.843807:0.489849:0.843807:0.473351:0.835311:0.473351:0.000000
2:@0.835311:0.506187:0.843807:0.506187:0.843807:0.489690:0.835311:0.489690:0.000000
Saberes previos:@0.199646:0.115710:0.307805:0.115710:0.307805:0.100238:0.199646:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo son los elemen-:@0.199884:0.144338:0.348217:0.144338:0.348217:0.129274:0.199884:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tos de  ?:@0.153341:0.160180:0.217432:0.160180:0.217432:0.145116:0.153341:0.145116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.195878:0.159177:0.207973:0.159177:0.207973:0.147484:0.195878:0.147484:0.000000
2:@0.207804:0.154379:0.212327:0.154379:0.212327:0.145597:0.207804:0.145597:0.000000
Desequilibrio cognitivo:@0.199646:0.206348:0.363493:0.206348:0.363493:0.190875:0.199646:0.190875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuántos elementos tie-:@0.199884:0.234975:0.355643:0.234975:0.355643:0.219912:0.199884:0.219912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ne una terna elemento de  ?:@0.153341:0.250817:0.346348:0.250817:0.346348:0.235754:0.153341:0.235754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.324795:0.249814:0.336890:0.249814:0.336890:0.238121:0.324795:0.238121:0.000000
3:@0.336722:0.245017:0.341245:0.245017:0.341245:0.236235:0.336722:0.236235:0.000000
Diseño CADD, www.esquemat.es:@0.386271:0.802685:0.386271:0.710199:0.374802:0.710199:0.374802:0.802685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.199770:0.343456:0.346555:0.343456:0.346555:0.327984:0.199770:0.327984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y Física:@0.200008:0.346405:0.338227:0.346405:0.338227:0.330932:0.200008:0.330932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Muchas de las aplicaciones en :@0.153465:0.361824:0.352334:0.361824:0.352334:0.346761:0.153465:0.346761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el campo de la física y, en estos :@0.153465:0.377666:0.356643:0.377666:0.356643:0.362603:0.153465:0.362603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
últimos años, en la computa-:@0.153465:0.393508:0.342485:0.393508:0.342485:0.378445:0.153465:0.378445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción gráfica, por ejemplo, el :@0.153465:0.409350:0.335236:0.409350:0.335236:0.394287:0.153465:0.394287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diseño asistido por computa-:@0.153465:0.425192:0.344226:0.425192:0.344226:0.410129:0.153465:0.410129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dora y la simulación numérica, :@0.153465:0.441034:0.355273:0.441034:0.355273:0.425971:0.153465:0.425971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
requieren del conocimiento :@0.153465:0.456876:0.337226:0.456876:0.337226:0.441813:0.153465:0.441813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemático de los espacios :@0.153465:0.472718:0.335592:0.472718:0.335592:0.457655:0.153465:0.457655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectoriales.:@0.153465:0.488560:0.225036:0.488560:0.225036:0.473497:0.153465:0.473497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Así, por ejemplo, en física, el :@0.153465:0.511531:0.338473:0.511531:0.338473:0.496468:0.153465:0.496468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
movimiento de una partícula o :@0.153465:0.527373:0.359127:0.527373:0.359127:0.512310:0.153465:0.512310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un cuerpo se determina por :@0.153465:0.543215:0.359371:0.543215:0.359371:0.528152:0.153465:0.528152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el vector de posición, la veloci-:@0.153465:0.559057:0.352140:0.559057:0.352140:0.543994:0.153465:0.543994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dad, la aceleración, las fuerzas :@0.153465:0.574899:0.348077:0.574899:0.348077:0.559836:0.153465:0.559836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que obran sobre dicho movi-:@0.153465:0.590741:0.342839:0.590741:0.342839:0.575678:0.153465:0.575678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miento, entre otros elementos.:@0.153465:0.606583:0.351507:0.606583:0.351507:0.591520:0.153465:0.591520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.153471:0.826464:0.164952:0.826464:0.164952:0.816440:0.153471:0.816440:0.000000
 :@0.164952:0.827172:0.167833:0.827172:0.167833:0.815695:0.164952:0.815695:0.000000
Torre Eiffel.:@0.167833:0.827172:0.221829:0.827172:0.221829:0.815695:0.167833:0.815695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga escribe:@0.153470:0.854182:0.265602:0.854182:0.265602:0.838710:0.153470:0.838710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.201101:0.853760:0.215807:0.853760:0.215807:0.838696:0.201101:0.838696:0.000000:0.000000:0.000000
 con tus :@0.265606:0.853760:0.321349:0.853760:0.321349:0.838696:0.265606:0.838696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
palabras qué es un sistemas de :@0.153470:0.869602:0.355192:0.869602:0.355192:0.854538:0.153470:0.854538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenadas espaciales.:@0.153470:0.885444:0.307257:0.885444:0.307257:0.870380:0.153470:0.870380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.199770:0.317171:0.346555:0.317171:0.346555:0.301699:0.199770:0.301699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000