136:@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
El conjunto de :@0.287495:0.377740:0.437149:0.377740:0.437149:0.356230:0.287495:0.356230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los elementos de :@0.287495:0.404085:0.423344:0.404085:0.423344:0.387696:0.287495:0.387696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.424466:0.405361:0.437771:0.405361:0.437771:0.388613:0.424466:0.388613:0.000000
3:@0.438393:0.396829:0.443604:0.396829:0.443604:0.387331:0.438393:0.387331:0.000000
 son ternas ordenadas, así :@0.443440:0.404085:0.639400:0.404085:0.639400:0.387696:0.443440:0.387696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xy z:@0.649210:0.403441:0.687281:0.403441:0.687281:0.387080:0.649210:0.387080:0.000000:0.000000:0.000000:0.000000
,,:@0.658166:0.403441:0.677072:0.403441:0.677072:0.387053:0.658166:0.387053:0.000000:0.000000
(:@0.640730:0.404775:0.646866:0.404775:0.646866:0.383123:0.640730:0.383123:0.000000
):@0.689618:0.404775:0.695755:0.404775:0.695755:0.383123:0.689618:0.383123:0.000000
∈:@0.697530:0.403027:0.710669:0.403027:0.710669:0.386084:0.697530:0.386084:0.000000
:@0.712918:0.404313:0.726222:0.404313:0.726222:0.387564:0.712918:0.387564:0.000000
3:@0.726847:0.395779:0.732059:0.395779:0.732059:0.386281:0.726847:0.386281:0.000000
, donde   es la primera :@0.733099:0.404085:0.907683:0.404085:0.907683:0.387696:0.733099:0.387696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.795256:0.404085:0.802719:0.404085:0.802719:0.387724:0.795256:0.387724:0.000000
componente,   la segunda y   la tercera componente.:@0.287500:0.420682:0.680411:0.420682:0.680411:0.404293:0.287500:0.404293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.390859:0.420682:0.398341:0.420682:0.398341:0.404320:0.390859:0.404320:0.000000
z:@0.498753:0.420682:0.505995:0.420682:0.505995:0.404320:0.498753:0.404320:0.000000
Por ejemplo, el vector: :@0.596440:0.444401:0.763024:0.444401:0.763024:0.428012:0.596440:0.428012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.762833:0.444534:0.772157:0.444534:0.772157:0.428173:0.762833:0.428173:0.000000
:@0.764141:0.433304:0.771697:0.433304:0.771697:0.416555:0.764141:0.416555:0.000000
:@0.858689:0.445405:0.871993:0.445405:0.871993:0.428657:0.858689:0.428657:0.000000
=:@0.776498:0.444119:0.786615:0.444119:0.786615:0.427177:0.776498:0.427177:0.000000
(:@0.790161:0.445869:0.796298:0.445869:0.796298:0.424217:0.790161:0.424217:0.000000
):@0.835401:0.445869:0.841537:0.445869:0.841537:0.424217:0.835401:0.424217:0.000000
∈:@0.843298:0.444119:0.856437:0.444119:0.856437:0.427177:0.843298:0.427177:0.000000
32 4:@0.797229:0.444534:0.834232:0.444534:0.834232:0.428145:0.797229:0.428145:0.000000:0.000000:0.000000:0.000000
3:@0.872615:0.436873:0.877826:0.436873:0.877826:0.427375:0.872615:0.427375:0.000000
,,:@0.805867:0.444534:0.822783:0.444534:0.822783:0.428145:0.805867:0.428145:0.000000:0.000000
El eje   es horizontal.:@0.596426:0.468130:0.747128:0.468130:0.747128:0.451741:0.596426:0.451741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.638755:0.468130:0.646218:0.468130:0.646218:0.451768:0.638755:0.451768:0.000000
El eje   es la profundidad lateral.:@0.596426:0.484726:0.829958:0.484726:0.829958:0.468337:0.596426:0.468337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.638755:0.484726:0.646236:0.484726:0.646236:0.468365:0.638755:0.468365:0.000000
El eje   es vertical.:@0.596426:0.501322:0.725971:0.501322:0.725971:0.484933:0.596426:0.484933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.638755:0.501322:0.645997:0.501322:0.645997:0.484961:0.638755:0.484961:0.000000
La representación del vector :@0.596426:0.525041:0.808451:0.525041:0.808451:0.508652:0.596426:0.508652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.596250:0.541772:0.605575:0.541772:0.605575:0.525411:0.596250:0.525411:0.000000
:@0.597559:0.530542:0.605114:0.530542:0.605114:0.513794:0.597559:0.513794:0.000000
:@0.692106:0.542644:0.705411:0.542644:0.705411:0.525895:0.692106:0.525895:0.000000
=:@0.609914:0.541357:0.620031:0.541357:0.620031:0.524415:0.609914:0.524415:0.000000
(:@0.623579:0.543107:0.629715:0.543107:0.629715:0.521455:0.623579:0.521455:0.000000
):@0.668819:0.543107:0.674955:0.543107:0.674955:0.521455:0.668819:0.521455:0.000000
∈:@0.676714:0.541357:0.689853:0.541357:0.689853:0.524415:0.676714:0.524415:0.000000
32 4:@0.630645:0.541772:0.667648:0.541772:0.667648:0.525383:0.630645:0.525383:0.000000:0.000000:0.000000:0.000000
3:@0.706031:0.534110:0.711242:0.534110:0.711242:0.524612:0.706031:0.524612:0.000000
,,:@0.639284:0.541772:0.656201:0.541772:0.656201:0.525383:0.639284:0.525383:0.000000:0.000000
 es la unión del origen :@0.711576:0.541648:0.877994:0.541648:0.877994:0.525259:0.711576:0.525259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con el punto.:@0.596421:0.558244:0.693330:0.558244:0.693330:0.541855:0.596421:0.541855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Norma o magnitud de un vector:@0.287495:0.587351:0.564569:0.587351:0.564569:0.568914:0.287495:0.568914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La norma de un vector :@0.287495:0.611130:0.465377:0.611130:0.465377:0.594741:0.287495:0.594741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.467386:0.610902:0.476710:0.610902:0.476710:0.594541:0.467386:0.594541:0.000000
x yz:@0.503191:0.610902:0.541271:0.610902:0.541271:0.594541:0.503191:0.594541:0.000000:0.000000:0.000000:0.000000
:@0.468696:0.599672:0.476251:0.599672:0.476251:0.582924:0.468696:0.582924:0.000000
:@0.566907:0.611774:0.580212:0.611774:0.580212:0.595025:0.566907:0.595025:0.000000
=:@0.481051:0.610488:0.491168:0.610488:0.491168:0.593545:0.481051:0.593545:0.000000
(:@0.494714:0.612237:0.500851:0.612237:0.500851:0.590585:0.494714:0.590585:0.000000
):@0.543603:0.612237:0.549739:0.612237:0.549739:0.590585:0.543603:0.590585:0.000000
∈:@0.551515:0.610488:0.564654:0.610488:0.564654:0.593545:0.551515:0.593545:0.000000
,,:@0.512147:0.610902:0.531053:0.610902:0.531053:0.594514:0.512147:0.594514:0.000000:0.000000
3:@0.580832:0.603241:0.586043:0.603241:0.586043:0.593743:0.580832:0.593743:0.000000
 es la longitud del vector, y siempre es un :@0.585923:0.611130:0.907706:0.611130:0.907706:0.594741:0.585923:0.594741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número positivo; se calcula así: :@0.287487:0.629593:0.516725:0.629593:0.516725:0.613205:0.287487:0.613205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.521763:0.629727:0.531087:0.629727:0.531087:0.613365:0.521763:0.613365:0.000000
x:@0.568458:0.629727:0.575921:0.629727:0.575921:0.613365:0.568458:0.613365:0.000000
y:@0.602435:0.629727:0.609917:0.629727:0.609917:0.613365:0.602435:0.613365:0.000000
z:@0.635845:0.629727:0.643087:0.629727:0.643087:0.613365:0.635845:0.613365:0.000000
:@0.523068:0.618497:0.530623:0.618497:0.530623:0.601748:0.523068:0.601748:0.000000
=:@0.540870:0.629312:0.550987:0.629312:0.550987:0.612370:0.540870:0.612370:0.000000
+:@0.587621:0.629312:0.597738:0.629312:0.597738:0.612370:0.587621:0.612370:0.000000
+:@0.621602:0.629312:0.631719:0.629312:0.631719:0.612370:0.621602:0.612370:0.000000
2:@0.577516:0.622064:0.582728:0.622064:0.582728:0.612566:0.577516:0.612566:0.000000
2:@0.611488:0.622064:0.616700:0.622064:0.616700:0.612566:0.611488:0.612566:0.000000
2:@0.644574:0.622064:0.649785:0.622064:0.649785:0.612566:0.644574:0.612566:0.000000
En el caso anterior, para el vector: :@0.287495:0.653312:0.535214:0.653312:0.535214:0.636924:0.287495:0.636924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.535037:0.653441:0.544362:0.653441:0.544362:0.637079:0.535037:0.637079:0.000000
:@0.536346:0.642210:0.543901:0.642210:0.543901:0.625462:0.536346:0.625462:0.000000
:@0.630893:0.654312:0.644198:0.654312:0.644198:0.637564:0.630893:0.637564:0.000000
=:@0.548700:0.653026:0.558817:0.653026:0.558817:0.636084:0.548700:0.636084:0.000000
(:@0.562365:0.654776:0.568502:0.654776:0.568502:0.633124:0.562365:0.633124:0.000000
):@0.607605:0.654776:0.613742:0.654776:0.613742:0.633124:0.607605:0.633124:0.000000
∈:@0.615501:0.653026:0.628640:0.653026:0.628640:0.636084:0.615501:0.636084:0.000000
32 4:@0.569432:0.653441:0.606434:0.653441:0.606434:0.637052:0.569432:0.637052:0.000000:0.000000:0.000000:0.000000
3:@0.644817:0.645780:0.650029:0.645780:0.650029:0.636282:0.644817:0.636282:0.000000
,,:@0.578071:0.653441:0.594987:0.653441:0.594987:0.637052:0.578071:0.637052:0.000000:0.000000
 la norma es:@0.650369:0.653312:0.739262:0.653312:0.739262:0.636924:0.650369:0.636924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.293530:0.672953:0.302854:0.672953:0.302854:0.656591:0.293530:0.656591:0.000000
:@0.294838:0.661723:0.302393:0.661723:0.302393:0.644974:0.294838:0.644974:0.000000
=:@0.312637:0.672538:0.322754:0.672538:0.322754:0.655596:0.312637:0.655596:0.000000
+:@0.357656:0.672538:0.367773:0.672538:0.367773:0.655596:0.357656:0.655596:0.000000
+:@0.389647:0.672538:0.399763:0.672538:0.399763:0.655596:0.389647:0.655596:0.000000
=:@0.425083:0.672538:0.435200:0.672538:0.435200:0.655596:0.425083:0.655596:0.000000
++:@0.463523:0.672538:0.499604:0.672538:0.499604:0.655596:0.463523:0.655596:0.000000:0.000000
=:@0.524924:0.672538:0.535041:0.672538:0.535041:0.655596:0.524924:0.655596:0.000000
3:@0.338823:0.672953:0.347816:0.672953:0.347816:0.656564:0.338823:0.656564:0.000000
2:@0.370813:0.672953:0.379806:0.672953:0.379806:0.656564:0.370813:0.656564:0.000000
4:@0.403375:0.672953:0.412368:0.672953:0.412368:0.656564:0.403375:0.656564:0.000000
9 416:@0.451269:0.672953:0.519360:0.672953:0.519360:0.656564:0.451269:0.656564:0.000000:0.000000:0.000000:0.000000:0.000000
29:@0.551093:0.672953:0.568989:0.672953:0.568989:0.656564:0.551093:0.656564:0.000000:0.000000
2:@0.347556:0.665290:0.352768:0.665290:0.352768:0.655792:0.347556:0.655792:0.000000
2:@0.379542:0.665290:0.384753:0.665290:0.384753:0.655792:0.379542:0.655792:0.000000
2:@0.412681:0.665290:0.417892:0.665290:0.417892:0.655792:0.412681:0.655792:0.000000
Distancia entre dos puntos en  3:@0.287495:0.705683:0.570580:0.705683:0.570580:0.687246:0.287495:0.687246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.549472:0.704747:0.563986:0.704747:0.563986:0.690716:0.549472:0.690716:0.000000
Dados dos vectores en :@0.287495:0.729152:0.458135:0.729152:0.458135:0.712763:0.287495:0.712763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.459259:0.729096:0.469155:0.729096:0.469155:0.712735:0.459259:0.712735:0.000000
x yz:@0.495064:0.729096:0.541520:0.729096:0.541520:0.712735:0.495064:0.712735:0.000000:0.000000:0.000000:0.000000
B:@0.570618:0.729096:0.579463:0.729096:0.579463:0.712735:0.570618:0.712735:0.000000
x yz:@0.606165:0.729096:0.657025:0.729096:0.657025:0.712735:0.606165:0.712735:0.000000:0.000000:0.000000:0.000000
:@0.459836:0.717872:0.467391:0.717872:0.467391:0.701124:0.459836:0.701124:0.000000
:@0.571599:0.717872:0.579155:0.717872:0.579155:0.701124:0.571599:0.701124:0.000000
:@0.689029:0.729974:0.702333:0.729974:0.702333:0.713225:0.689029:0.713225:0.000000
=:@0.472923:0.728688:0.483039:0.728688:0.483039:0.711746:0.472923:0.711746:0.000000
(:@0.486586:0.730438:0.492722:0.730438:0.492722:0.708785:0.486586:0.708785:0.000000
):@0.548042:0.730438:0.554179:0.730438:0.554179:0.708785:0.548042:0.708785:0.000000
=:@0.584013:0.728688:0.594130:0.728688:0.594130:0.711746:0.584013:0.711746:0.000000
(:@0.597676:0.730438:0.603813:0.730438:0.603813:0.708785:0.597676:0.708785:0.000000
):@0.665729:0.730438:0.671866:0.730438:0.671866:0.708785:0.665729:0.708785:0.000000
∈:@0.673638:0.728688:0.686777:0.728688:0.686777:0.711746:0.673638:0.711746:0.000000
1:@0.502658:0.731106:0.507870:0.731106:0.507870:0.721608:0.502658:0.721608:0.000000
1:@0.522554:0.731106:0.527766:0.731106:0.527766:0.721608:0.522554:0.721608:0.000000
1:@0.541554:0.731106:0.546765:0.731106:0.546765:0.721608:0.541554:0.721608:0.000000
2:@0.614432:0.731106:0.619643:0.731106:0.619643:0.721608:0.614432:0.721608:0.000000
2:@0.636517:0.731106:0.641729:0.731106:0.641729:0.721608:0.636517:0.721608:0.000000
2:@0.657716:0.731106:0.662928:0.731106:0.662928:0.721608:0.657716:0.721608:0.000000
3:@0.702955:0.721440:0.708167:0.721440:0.708167:0.711942:0.702955:0.711942:0.000000
,,:@0.508208:0.729103:0.531317:0.729103:0.531317:0.712714:0.508208:0.712714:0.000000:0.000000
;  :@0.556010:0.729103:0.569996:0.729103:0.569996:0.712714:0.556010:0.712714:0.000000:0.000000:0.000000
,:@0.621501:0.729103:0.624708:0.729103:0.624708:0.712714:0.621501:0.712714:0.000000
,:@0.643596:0.729103:0.646803:0.729103:0.646803:0.712714:0.643596:0.712714:0.000000
 la distancia o norma entre :@0.708885:0.729158:0.907683:0.729158:0.907683:0.712769:0.708885:0.712769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los dos vectores es:  (:@0.287500:0.752462:0.449370:0.752034:0.449370:0.735646:0.287500:0.736073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dAB:@0.434702:0.752034:0.469457:0.752034:0.469457:0.735673:0.434702:0.735673:0.000000:0.000000:0.000000
x:@0.511453:0.752034:0.518916:0.752034:0.518916:0.735673:0.511453:0.735673:0.000000
x:@0.544052:0.752034:0.551515:0.752034:0.551515:0.735673:0.544052:0.735673:0.000000
y:@0.594212:0.752034:0.601693:0.752034:0.601693:0.735673:0.594212:0.735673:0.000000
y:@0.627087:0.752034:0.634568:0.752034:0.634568:0.735673:0.627087:0.735673:0.000000
z:@0.678758:0.752034:0.686000:0.752034:0.686000:0.735673:0.678758:0.735673:0.000000
z:@0.710748:0.752034:0.717990:0.752034:0.717990:0.735673:0.710748:0.735673:0.000000
):@0.470452:0.752034:0.475335:0.752034:0.475335:0.735646:0.470452:0.735646:0.000000
(:@0.504801:0.752034:0.509684:0.752034:0.509684:0.735646:0.504801:0.735646:0.000000
):@0.557522:0.752034:0.562406:0.752034:0.562406:0.735646:0.557522:0.735646:0.000000
=:@0.478947:0.751620:0.489064:0.751620:0.489064:0.734677:0.478947:0.734677:0.000000
−:@0.529826:0.751620:0.539942:0.751620:0.539942:0.734677:0.529826:0.734677:0.000000
+:@0.572338:0.751620:0.582455:0.751620:0.582455:0.734677:0.572338:0.734677:0.000000
−:@0.612602:0.751620:0.622719:0.751620:0.622719:0.734677:0.612602:0.734677:0.000000
(:@0.585474:0.753369:0.591610:0.753369:0.591610:0.731717:0.585474:0.731717:0.000000
) (:@0.641180:0.753369:0.676734:0.753369:0.676734:0.731717:0.641180:0.731717:0.000000:0.000000:0.000000
+:@0.657457:0.751620:0.667574:0.751620:0.667574:0.734677:0.657457:0.734677:0.000000
−:@0.696818:0.751620:0.706935:0.751620:0.706935:0.734677:0.696818:0.734677:0.000000
):@0.724517:0.753369:0.730653:0.753369:0.730653:0.731717:0.724517:0.731717:0.000000
2:@0.519721:0.754038:0.524932:0.754038:0.524932:0.744540:0.519721:0.744540:0.000000
1:@0.551653:0.754038:0.556864:0.754038:0.556864:0.744540:0.551653:0.744540:0.000000
2:@0.562226:0.744372:0.567437:0.744372:0.567437:0.734874:0.562226:0.734874:0.000000
2:@0.602488:0.754038:0.607700:0.754038:0.607700:0.744540:0.602488:0.744540:0.000000
1:@0.634687:0.754038:0.639899:0.754038:0.639899:0.744540:0.634687:0.744540:0.000000
2:@0.647353:0.742448:0.652565:0.742448:0.652565:0.732950:0.647353:0.732950:0.000000
2:@0.686722:0.754038:0.691933:0.754038:0.691933:0.744540:0.686722:0.744540:0.000000
1:@0.718024:0.754038:0.723235:0.754038:0.723235:0.744540:0.718024:0.744540:0.000000
2:@0.730697:0.742449:0.735909:0.742449:0.735909:0.732950:0.730697:0.732950:0.000000
Operaciones en  3:@0.287495:0.785137:0.448097:0.785137:0.448097:0.766700:0.287495:0.766700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.426989:0.784201:0.441504:0.784201:0.441504:0.770170:0.426989:0.770170:0.000000
Adición. :@0.287495:0.808605:0.356488:0.808605:0.356488:0.791705:0.287495:0.791705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean los vectores: :@0.357023:0.808605:0.491876:0.808605:0.491876:0.792217:0.357023:0.792217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.493560:0.808556:0.502884:0.808556:0.502884:0.792195:0.493560:0.792195:0.000000
a bc:@0.528222:0.808556:0.565359:0.808556:0.565359:0.792195:0.528222:0.792195:0.000000:0.000000:0.000000:0.000000
v:@0.589518:0.808556:0.597257:0.808556:0.597257:0.792195:0.589518:0.792195:0.000000
x yz:@0.624751:0.808556:0.662823:0.808556:0.662823:0.792195:0.624751:0.792195:0.000000:0.000000:0.000000:0.000000
:@0.494868:0.797326:0.502424:0.797326:0.502424:0.780578:0.494868:0.780578:0.000000
:@0.590508:0.797326:0.598063:0.797326:0.598063:0.780578:0.590508:0.780578:0.000000
:@0.688469:0.809428:0.701774:0.809428:0.701774:0.792679:0.688469:0.792679:0.000000
=:@0.507233:0.808142:0.517350:0.808142:0.517350:0.791199:0.507233:0.791199:0.000000
(:@0.520888:0.809891:0.527025:0.809891:0.527025:0.788239:0.520888:0.788239:0.000000
):@0.567271:0.809891:0.573407:0.809891:0.573407:0.788239:0.567271:0.788239:0.000000
=:@0.602608:0.808142:0.612725:0.808142:0.612725:0.791199:0.602608:0.791199:0.000000
(:@0.616271:0.809891:0.622408:0.809891:0.622408:0.788239:0.616271:0.788239:0.000000
):@0.665160:0.809891:0.671296:0.809891:0.671296:0.788239:0.665160:0.788239:0.000000
∈:@0.673072:0.808142:0.686211:0.808142:0.686211:0.791199:0.673072:0.791199:0.000000
,,:@0.537744:0.808556:0.555564:0.808556:0.555564:0.792168:0.537744:0.792168:0.000000:0.000000
;  :@0.575226:0.808556:0.589213:0.808556:0.589213:0.792168:0.575226:0.792168:0.000000:0.000000:0.000000
, ,:@0.633697:0.808556:0.652622:0.808556:0.652622:0.792168:0.633697:0.792168:0.000000:0.000000:0.000000
3:@0.702389:0.800894:0.707600:0.800894:0.707600:0.791396:0.702389:0.791396:0.000000
 entonces la adición impli-:@0.708497:0.808605:0.903664:0.808605:0.903664:0.792217:0.708497:0.792217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ca sumar componente a componente. :@0.287499:0.825257:0.573658:0.825257:0.573658:0.808868:0.287499:0.808868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
uv:@0.575818:0.825202:0.609208:0.825202:0.609208:0.808841:0.575818:0.808841:0.000000:0.000000
ab c:@0.635542:0.825202:0.672673:0.825202:0.672673:0.808841:0.635542:0.808841:0.000000:0.000000:0.000000:0.000000
x yz:@0.705327:0.825202:0.743399:0.825202:0.743399:0.808841:0.705327:0.808841:0.000000:0.000000:0.000000:0.000000
ax by cz:@0.776679:0.825202:0.892659:0.825212:0.892659:0.808851:0.776679:0.808841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.577123:0.813982:0.610016:0.813982:0.610016:0.797233:0.577123:0.797233:0.000000:0.000000
+=:@0.588640:0.824797:0.624666:0.824797:0.624666:0.807855:0.588640:0.807855:0.000000:0.000000
(:@0.628221:0.826547:0.634357:0.826547:0.634357:0.804895:0.628221:0.804895:0.000000
) (:@0.674603:0.826547:0.702990:0.826547:0.702990:0.804895:0.674603:0.804895:0.000000:0.000000:0.000000
+:@0.683713:0.824797:0.693830:0.824797:0.693830:0.807855:0.683713:0.807855:0.000000
) (:@0.745742:0.826547:0.775496:0.826547:0.775496:0.804895:0.745742:0.804895:0.000000:0.000000:0.000000
=:@0.755696:0.824797:0.765813:0.824797:0.765813:0.807855:0.755696:0.807855:0.000000
+:@0.789253:0.824797:0.799370:0.824797:0.799370:0.807855:0.789253:0.807855:0.000000
+:@0.830402:0.824797:0.840519:0.824797:0.840519:0.807855:0.830402:0.807855:0.000000
+:@0.871182:0.824797:0.881299:0.824797:0.881299:0.807855:0.871182:0.807855:0.000000
):@0.894999:0.826547:0.901136:0.826547:0.901136:0.804895:0.894999:0.804895:0.000000
,,:@0.645077:0.825212:0.662897:0.825212:0.662897:0.808823:0.645077:0.808823:0.000000:0.000000
,,:@0.714291:0.825212:0.733198:0.825212:0.733198:0.808823:0.714291:0.808823:0.000000:0.000000
,:@0.812769:0.825212:0.815975:0.825212:0.815975:0.808823:0.812769:0.808823:0.000000
,:@0.854175:0.825212:0.857382:0.825212:0.857382:0.808823:0.854175:0.808823:0.000000
Producto de un escalar por un vector en  :@0.287507:0.848986:0.607752:0.848986:0.607752:0.832086:0.287507:0.832086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.607329:0.850262:0.620634:0.850262:0.620634:0.833514:0.607329:0.833514:0.000000
3:@0.621255:0.841730:0.626467:0.841730:0.626467:0.832232:0.621255:0.832232:0.000000
.:@0.626303:0.848986:0.630652:0.848986:0.630652:0.832086:0.626303:0.832086:0.000000
 Sea :@0.630652:0.848986:0.664208:0.848986:0.664208:0.832597:0.630652:0.832597:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.664505:0.848503:0.676133:0.848503:0.676133:0.831561:0.664505:0.831561:0.000000
∈:@0.676446:0.848503:0.621624:0.848503:0.621624:0.831561:0.676446:0.831561:0.000000
=:@0.744407:0.848503:0.689585:0.848503:0.689585:0.831561:0.744407:0.831561:0.000000
(:@0.758069:0.850243:0.717823:0.850243:0.717823:0.828591:0.758069:0.828591:0.000000
):@0.804451:0.850243:0.764205:0.850243:0.764205:0.828591:0.804451:0.828591:0.000000
∈:@0.812358:0.848503:0.825497:0.848503:0.825497:0.831561:0.812358:0.831561:0.000000
  y  :@0.706242:0.848918:0.730492:0.848918:0.730492:0.832529:0.706242:0.832529:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.730732:0.848918:0.740056:0.848918:0.740056:0.832557:0.730732:0.832557:0.000000
a bc:@0.765394:0.848918:0.802545:0.848918:0.802545:0.832557:0.765394:0.832557:0.000000:0.000000:0.000000:0.000000
,,:@0.774921:0.848918:0.792741:0.848918:0.792741:0.832529:0.774921:0.832529:0.000000:0.000000
, el pro-:@0.848743:0.848918:0.903637:0.848986:0.903637:0.832597:0.848743:0.832529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.841675:0.841247:0.846886:0.841247:0.846886:0.831749:0.841675:0.831749:0.000000
ducto de un escalar por un vector se define como: :@0.287490:0.865583:0.660276:0.865583:0.660276:0.849194:0.287490:0.849194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.582806:0.865583:0.586842:0.865583:0.586842:0.849194:0.582806:0.849194:0.000000
α      α:@0.661955:0.864674:0.709162:0.864674:0.709162:0.848961:0.661955:0.848961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α   α   α:@0.780108:0.864674:0.837416:0.864674:0.837416:0.848961:0.780108:0.848961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.672142:0.865059:0.680790:0.865059:0.680790:0.849884:0.672142:0.849884:0.000000
a bc:@0.717059:0.865059:0.751498:0.865059:0.751498:0.849884:0.717059:0.849884:0.000000:0.000000:0.000000:0.000000
a b c:@0.790808:0.865059:0.844356:0.865059:0.844356:0.849884:0.790808:0.849884:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.673355:0.854631:0.680363:0.854631:0.680363:0.839097:0.673355:0.839097:0.000000
 =:@0.681746:0.865059:0.695676:0.865059:0.695676:0.849859:0.681746:0.849859:0.000000:0.000000
, ,:@0.725877:0.865059:0.742404:0.865059:0.742404:0.849859:0.725877:0.849859:0.000000:0.000000:0.000000
,:@0.799643:0.865059:0.802617:0.865059:0.802617:0.849859:0.799643:0.849859:0.000000
,:@0.822255:0.865059:0.825229:0.865059:0.825229:0.849859:0.822255:0.849859:0.000000
(:@0.710264:0.866289:0.672936:0.866289:0.672936:0.846207:0.710264:0.846207:0.000000
):@0.753283:0.866289:0.715955:0.866289:0.715955:0.846207:0.753283:0.846207:0.000000
=:@0.762510:0.864674:0.771893:0.864674:0.771893:0.848961:0.762510:0.848961:0.000000
(:@0.775181:0.866289:0.711105:0.866289:0.711105:0.846207:0.775181:0.846207:0.000000
):@0.844949:0.866289:0.780873:0.866289:0.780873:0.846207:0.844949:0.846207:0.000000
Producto escalar en :@0.287495:0.889307:0.447834:0.889307:0.447834:0.872406:0.287495:0.872406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.447853:0.890584:0.461157:0.890584:0.461157:0.873836:0.447853:0.873836:0.000000
3:@0.461779:0.882050:0.466991:0.882050:0.466991:0.872552:0.461779:0.872552:0.000000
. El producto escalar o producto punto entre dos vectores:@0.466826:0.889307:0.888947:0.889307:0.888947:0.872918:0.466826:0.872918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.289700:0.906276:0.299024:0.906276:0.299024:0.889915:0.289700:0.889915:0.000000
a bc:@0.324362:0.906276:0.361494:0.906276:0.361494:0.889915:0.324362:0.889915:0.000000:0.000000:0.000000:0.000000
v:@0.385653:0.906276:0.393392:0.906276:0.393392:0.889915:0.385653:0.889915:0.000000
x yz:@0.420886:0.906276:0.458958:0.906276:0.458958:0.889915:0.420886:0.889915:0.000000:0.000000:0.000000:0.000000
:@0.291003:0.895049:0.298559:0.895049:0.298559:0.878300:0.291003:0.878300:0.000000
:@0.386643:0.895049:0.394198:0.895049:0.394198:0.878300:0.386643:0.878300:0.000000
:@0.484597:0.907150:0.497902:0.907150:0.497902:0.890402:0.484597:0.890402:0.000000
=:@0.303358:0.905864:0.313475:0.905864:0.313475:0.888922:0.303358:0.888922:0.000000
(:@0.317022:0.907614:0.323158:0.907614:0.323158:0.885962:0.317022:0.885962:0.000000
):@0.363404:0.907614:0.369540:0.907614:0.369540:0.885962:0.363404:0.885962:0.000000
=:@0.398741:0.905864:0.408858:0.905864:0.408858:0.888922:0.398741:0.888922:0.000000
(:@0.412405:0.907614:0.418541:0.907614:0.418541:0.885962:0.412405:0.885962:0.000000
):@0.461293:0.907614:0.467430:0.907614:0.467430:0.885962:0.461293:0.885962:0.000000
∈:@0.469205:0.905864:0.482344:0.905864:0.482344:0.888922:0.469205:0.888922:0.000000
,,:@0.333878:0.906279:0.351697:0.906279:0.351697:0.889890:0.333878:0.889890:0.000000:0.000000
;  :@0.371360:0.906279:0.385346:0.906279:0.385346:0.889890:0.371360:0.889890:0.000000:0.000000:0.000000
, ,:@0.429830:0.906279:0.448756:0.906279:0.448756:0.889890:0.429830:0.889890:0.000000:0.000000:0.000000
3:@0.498524:0.898618:0.503735:0.898618:0.503735:0.889120:0.498524:0.889120:0.000000
es un número y se define como: :@0.506952:0.906151:0.746139:0.906151:0.746139:0.889762:0.506952:0.889762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.668669:0.906151:0.672705:0.906151:0.672705:0.889762:0.668669:0.889762:0.000000
uv:@0.748337:0.906141:0.774191:0.906141:0.774191:0.889779:0.748337:0.889779:0.000000:0.000000
ax by cz:@0.793466:0.906141:0.877423:0.906141:0.877423:0.889779:0.793466:0.889779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.749664:0.894910:0.775020:0.894910:0.775020:0.878162:0.749664:0.878162:0.000000:0.000000
⋅=:@0.760297:0.905726:0.789689:0.905726:0.789689:0.888784:0.760297:0.888784:0.000000:0.000000
+:@0.814695:0.905726:0.824812:0.905726:0.824812:0.888784:0.814695:0.888784:0.000000
+:@0.849044:0.905726:0.859161:0.905726:0.859161:0.888784:0.849044:0.888784:0.000000
.:@0.879932:0.906151:0.883139:0.906151:0.883139:0.889762:0.879932:0.889762:0.000000
Si el producto punto es cero (0) los vectores son perpendiculares.:@0.287502:0.922747:0.764901:0.922747:0.764901:0.906358:0.287502:0.906358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nidad de conocimientos:@0.306727:0.341480:0.480398:0.341480:0.480398:0.326116:0.306727:0.326116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.342266:0.297460:0.342266:0.297460:0.325130:0.284892:0.325130:0.000000
Pienso y progreso:@0.294883:0.288234:0.417347:0.288234:0.417347:0.272870:0.294883:0.272870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Para qué se emplean las grúas?:@0.294883:0.305627:0.507954:0.305627:0.507954:0.290728:0.294883:0.290728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En una obra, una grúa sostiene una viga de acero mediante tres cables que tiran de :@0.287495:0.168345:0.907694:0.168345:0.907694:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ella desde distintos puntos del techo. Cada cable ejerce una fuerza representada por :@0.287495:0.184941:0.907727:0.184941:0.907727:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un vector en el espacio.:@0.287495:0.201538:0.460437:0.201538:0.460437:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.410453:0.221955:0.418506:0.221955:0.418506:0.205594:0.410453:0.205594:0.000000
N:@0.507714:0.221955:0.518973:0.221955:0.518973:0.205594:0.507714:0.205594:0.000000
F:@0.538451:0.221955:0.546504:0.221955:0.546504:0.205594:0.538451:0.205594:0.000000
N:@0.635362:0.221955:0.646622:0.221955:0.646622:0.205594:0.635362:0.205594:0.000000
F:@0.666081:0.221955:0.674134:0.221955:0.674134:0.205594:0.666081:0.205594:0.000000
N:@0.762402:0.221955:0.773662:0.221955:0.773662:0.205594:0.762402:0.205594:0.000000
1:@0.416212:0.223959:0.421424:0.223959:0.421424:0.214461:0.416212:0.214461:0.000000
2:@0.544892:0.223959:0.550103:0.223959:0.550103:0.214461:0.544892:0.214461:0.000000
3:@0.672524:0.223959:0.677736:0.223959:0.677736:0.214461:0.672524:0.214461:0.000000
32 4      :@0.446367:0.221955:0.537837:0.221955:0.537837:0.205566:0.446367:0.205566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
134      :@0.587209:0.221955:0.665466:0.221955:0.665466:0.205566:0.587209:0.205566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
14 4   :@0.703064:0.221955:0.779110:0.221955:0.779110:0.205566:0.703064:0.205566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.411317:0.211347:0.420973:0.211347:0.420973:0.194599:0.411317:0.194599:0.000000:0.000000
:@0.539316:0.211347:0.551165:0.211347:0.551165:0.194599:0.539316:0.194599:0.000000:0.000000
:@0.666946:0.211347:0.678795:0.211347:0.678795:0.194599:0.666946:0.194599:0.000000:0.000000
=:@0.425654:0.221540:0.435771:0.221540:0.435771:0.204598:0.425654:0.204598:0.000000
−:@0.460685:0.221540:0.470802:0.221540:0.470802:0.204598:0.460685:0.204598:0.000000
(:@0.439299:0.223290:0.445435:0.223290:0.445435:0.201638:0.439299:0.201638:0.000000
):@0.495153:0.223290:0.501290:0.223290:0.501290:0.201638:0.495153:0.201638:0.000000
=−:@0.555834:0.221540:0.587253:0.221540:0.587253:0.204598:0.555834:0.204598:0.000000:0.000000
(:@0.569497:0.223290:0.575633:0.223290:0.575633:0.201638:0.569497:0.201638:0.000000
):@0.622790:0.223290:0.628926:0.223290:0.628926:0.201638:0.622790:0.201638:0.000000
=:@0.683465:0.221540:0.693582:0.221540:0.693582:0.204598:0.683465:0.204598:0.000000
−:@0.714774:0.221540:0.724890:0.221540:0.724890:0.204598:0.714774:0.204598:0.000000
(:@0.697128:0.223290:0.703265:0.223290:0.703265:0.201638:0.697128:0.201638:0.000000
):@0.749850:0.223290:0.755986:0.223290:0.755986:0.201638:0.749850:0.201638:0.000000
,:@0.455004:0.221955:0.458211:0.221955:0.458211:0.205566:0.455004:0.205566:0.000000
,:@0.479347:0.221955:0.482554:0.221955:0.482554:0.205566:0.479347:0.205566:0.000000
;:@0.519814:0.221955:0.523021:0.221955:0.523021:0.205566:0.519814:0.205566:0.000000
,:@0.593267:0.221955:0.596473:0.221955:0.596473:0.205566:0.593267:0.205566:0.000000
,:@0.606977:0.221955:0.610183:0.221955:0.610183:0.205566:0.606977:0.205566:0.000000
;:@0.647444:0.221955:0.650651:0.221955:0.650651:0.205566:0.647444:0.205566:0.000000
,:@0.709121:0.221955:0.712328:0.221955:0.712328:0.205566:0.709121:0.205566:0.000000
,:@0.734036:0.221955:0.737242:0.221955:0.737242:0.205566:0.734036:0.205566:0.000000
Determina la fuerza total que actúa sobre la viga como suma de los vectores. Luego, :@0.287495:0.241858:0.907775:0.241858:0.907775:0.225469:0.287495:0.225469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calcula la magnitud de la fuerza total para saber si la grúa puede resistir la carga.:@0.287495:0.258455:0.872105:0.258455:0.872105:0.242066:0.287495:0.242066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vectores en :@0.286308:0.075160:0.466051:0.075160:0.466051:0.041608:0.286308:0.041608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.490838:0.063066:0.501538:0.063066:0.501538:0.043505:0.490838:0.043505:0.000000
:@0.094760:0.108603:0.183816:0.108603:0.183816:0.011514:0.094760:0.011514:0.000000:0.000000
Un sistema de :@0.149598:0.494406:0.247832:0.494406:0.247832:0.479507:0.149598:0.479507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenadas :@0.157321:0.508236:0.247834:0.508236:0.247834:0.493337:0.157321:0.493337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tridimensional se :@0.130149:0.522067:0.247834:0.522067:0.247834:0.507168:0.130149:0.507168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
construye trazando un eje :@0.070359:0.535897:0.247834:0.535897:0.247834:0.520998:0.070359:0.520998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.101016:0.549727:0.107600:0.549727:0.107600:0.534853:0.101016:0.534853:0.000000
, perpendicular en el :@0.107600:0.549727:0.247832:0.549727:0.247832:0.534828:0.107600:0.534828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
origen de coordenadas a :@0.077781:0.563558:0.247832:0.563558:0.247832:0.548658:0.077781:0.548658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los ejes   y  .:@0.160822:0.577388:0.244165:0.577388:0.244165:0.562489:0.160822:0.562489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.212956:0.577388:0.241250:0.577388:0.241250:0.562514:0.212956:0.562514:0.000000:0.000000:0.000000
Cada punto viene :@0.125609:0.594776:0.247832:0.594776:0.247832:0.579877:0.125609:0.579877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinado por tres :@0.102088:0.608607:0.247832:0.608607:0.247832:0.593708:0.102088:0.593708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenadas   = ( ,  ,  ).:@0.083225:0.622437:0.244165:0.622437:0.244165:0.607538:0.083225:0.607538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.173738:0.622437:0.181712:0.622437:0.181712:0.607563:0.173738:0.607563:0.000000
x y z:@0.203474:0.622437:0.236811:0.622437:0.236811:0.607563:0.203474:0.607563:0.000000:0.000000:0.000000:0.000000:0.000000
Los ejes de coordenadas :@0.080612:0.639825:0.247832:0.639825:0.247832:0.624926:0.080612:0.624926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinan tres planos :@0.089691:0.653656:0.247832:0.653656:0.247832:0.638757:0.089691:0.638757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenados: XY, XZ y YZ. :@0.074212:0.667486:0.247832:0.667486:0.247832:0.652587:0.074212:0.652587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Estos planos coordenados :@0.069840:0.681316:0.247832:0.681316:0.247832:0.666417:0.069840:0.666417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dividen el espacio en :@0.103361:0.695147:0.247834:0.695147:0.247834:0.680248:0.103361:0.680248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ocho regiones llamadas :@0.085922:0.708977:0.247834:0.708977:0.247834:0.694078:0.085922:0.694078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
octantes. En el primer :@0.099592:0.722807:0.247832:0.722807:0.247832:0.707908:0.099592:0.707908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
octante, las tres :@0.140837:0.736638:0.247832:0.736638:0.247832:0.721739:0.140837:0.721739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenadas son :@0.129512:0.750468:0.247834:0.750468:0.247834:0.735569:0.129512:0.735569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
positivas.:@0.183421:0.764298:0.244164:0.764298:0.244164:0.749399:0.183421:0.749399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     Matemática:@0.115206:0.461965:0.222747:0.461965:0.222747:0.445064:0.115206:0.445064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es un sistema:@0.115742:0.190031:0.244164:0.190031:0.244164:0.175132:0.115742:0.175132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de coordenadas :@0.136414:0.203861:0.247834:0.203861:0.247834:0.188962:0.136414:0.188962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tridimensional?:@0.141808:0.217692:0.244166:0.217692:0.244166:0.202793:0.141808:0.202793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.161153:0.227756:0.161153:0.227756:0.144253:0.108521:0.144253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.068421:0.340345:0.068421:0.297520:0.056510:0.297520:0.056510:0.340345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el manejo de las grúas :@0.076177:0.379352:0.231620:0.379352:0.231620:0.365942:0.076177:0.365942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
están presenten los vectores :@0.076177:0.391923:0.250361:0.391923:0.250361:0.378514:0.076177:0.378514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en R .:@0.076177:0.404495:0.109399:0.404498:0.109399:0.391089:0.076177:0.391086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.102486:0.399550:0.106776:0.399550:0.106776:0.391732:0.102486:0.391732:0.000000
+Z:@0.144234:0.790583:0.157133:0.790583:0.157133:0.780172:0.144234:0.780172:0.000000:0.000000
+X:@0.209634:0.889913:0.222392:0.889913:0.222392:0.879501:0.209634:0.879501:0.000000:0.000000
3:@0.139379:0.780779:0.145102:0.780779:0.145102:0.770350:0.139379:0.770350:0.000000
+Y:@0.060400:0.889913:0.073065:0.889913:0.073065:0.879501:0.060400:0.879501:0.000000:0.000000
0:@0.132720:0.843667:0.138443:0.843667:0.138443:0.833237:0.132720:0.833237:0.000000
2:@0.215358:0.854369:0.221081:0.854369:0.221081:0.843939:0.215358:0.843939:0.000000
ZOY:@0.173154:0.799925:0.191776:0.799925:0.191776:0.789513:0.173154:0.789513:0.000000:0.000000:0.000000
XOZ:@0.092955:0.799925:0.112022:0.799925:0.112022:0.789513:0.092955:0.789513:0.000000:0.000000:0.000000
XOY:@0.049789:0.852767:0.068317:0.852767:0.068317:0.842355:0.049789:0.842355:0.000000:0.000000:0.000000
4:@0.074110:0.854369:0.079833:0.854369:0.079833:0.843939:0.074110:0.843939:0.000000
1:@0.155048:0.878783:0.160770:0.878783:0.160770:0.868354:0.155048:0.868354:0.000000
5:@0.138665:0.908883:0.144388:0.908883:0.144388:0.898453:0.138665:0.898453:0.000000
6:@0.228891:0.893586:0.234613:0.893586:0.234613:0.883157:0.228891:0.883157:0.000000
8:@0.049836:0.893586:0.055558:0.893586:0.055558:0.883157:0.049836:0.883157:0.000000
M.5.2.19.:@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
  :@0.353207:0.946788:0.359586:0.946788:0.359586:0.934496:0.353207:0.934496:0.000000:0.000000
Calcular el producto escalar entre dos vectores y la norma de un vector para determinar la distancia :@0.360415:0.946788:0.906578:0.946788:0.906578:0.934868:0.360415:0.934868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre dos puntos A y B en   como la norma del vector.:@0.298180:0.958103:0.593636:0.958103:0.593636:0.946184:0.298180:0.946184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.447498:0.953705:0.451310:0.953705:0.451310:0.946756:0.447498:0.946756:0.000000