144:@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 ó:@0.072616:0.090484:0.372170:0.090484:0.372170:0.064352:0.072616:0.064352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DUA:@0.773786:0.079446:0.817429:0.079446:0.817429:0.059195:0.773786:0.059195:0.000000:0.000000:0.000000 Acción y expresión:@0.721188:0.093905:0.870026:0.093905:0.870026:0.077005:0.721188:0.077005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 7.:@0.502373:0.145810:0.516600:0.145810:0.516600:0.128910:0.502373:0.128910:0.000000:0.000000 Sea la ecuación vectorial = (4, 2, 0) + (–4, –2, 0), :@0.516600:0.145810:0.907704:0.145810:0.907704:0.129422:0.516600:0.129422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.720966:0.145810:0.728429:0.145810:0.728429:0.129449:0.720966:0.129449:0.000000 t:@0.821684:0.145810:0.827065:0.145810:0.827065:0.129449:0.821684:0.129449:0.000000 obtén :@0.530878:0.162407:0.582272:0.162407:0.582272:0.145506:0.530878:0.145506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.582272:0.162407:0.790300:0.162407:0.790300:0.146018:0.582272:0.146018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8.:@0.502373:0.273281:0.516600:0.273281:0.516600:0.256380:0.502373:0.256380:0.000000:0.000000 Sea la ecuación vectorial = (5, 3, 6), :@0.516600:0.273281:0.806066:0.273281:0.806066:0.256892:0.516600:0.256892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.714918:0.273281:0.722381:0.273281:0.722381:0.256919:0.714918:0.256919:0.000000 t:@0.742214:0.273281:0.747595:0.273281:0.747595:0.256919:0.742214:0.256919:0.000000 obtén :@0.806066:0.273281:0.857461:0.273281:0.857461:0.256380:0.806066:0.256380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las :@0.857461:0.273281:0.880643:0.273281:0.880643:0.256892:0.857461:0.256892:0.000000:0.000000:0.000000:0.000000 ecuaciones paramétricas.:@0.530868:0.289877:0.715711:0.289877:0.715711:0.273488:0.530868:0.273488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 9.:@0.502373:0.402667:0.516600:0.402667:0.516600:0.385766:0.502373:0.385766:0.000000:0.000000 Sean los puntos = (1, 2, 1) y = (–1, 0, –1).:@0.516600:0.402667:0.860659:0.402667:0.860659:0.386278:0.516600:0.386278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.655507:0.403179:0.664776:0.403179:0.664776:0.386817:0.655507:0.386817:0.000000 q:@0.759392:0.403179:0.768661:0.403179:0.768661:0.386817:0.759392:0.386817:0.000000 a) Encuentra:@0.530859:0.428170:0.640317:0.428170:0.640317:0.411269:0.530859:0.411269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la ecuación vectorial de la recta que :@0.640317:0.428170:0.907684:0.428170:0.907684:0.411781:0.640317:0.411781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pasa por dichos puntos.:@0.559348:0.444766:0.734391:0.444766:0.734391:0.428378:0.559348:0.428378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b) :@0.530866:0.546734:0.550897:0.546734:0.550897:0.529833:0.530866:0.529833:0.000000:0.000000:0.000000 Con la ecuación vectorial del literal a) :@0.550897:0.546734:0.834979:0.546734:0.834979:0.530345:0.550897:0.530345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 determi-:@0.834850:0.546734:0.903640:0.546734:0.903640:0.529833:0.834850:0.529833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 na:@0.559355:0.563330:0.579257:0.563330:0.579257:0.546429:0.559355:0.546429:0.000000:0.000000 las ecuaciones paramétricas.:@0.579257:0.563330:0.791318:0.563330:0.791318:0.546941:0.579257:0.546941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 10.:@0.502373:0.674338:0.526477:0.674338:0.526477:0.657438:0.502373:0.657438:0.000000:0.000000:0.000000 Sean los puntos = (1, 1, 1) y = (2, –1, –3).:@0.526477:0.674338:0.860659:0.674338:0.860659:0.657949:0.526477:0.657949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.655507:0.674850:0.664776:0.674850:0.664776:0.658489:0.655507:0.658489:0.000000 q:@0.759392:0.674850:0.768661:0.674850:0.768661:0.658489:0.759392:0.658489:0.000000 a) Escribe:@0.530859:0.699841:0.616419:0.699841:0.616419:0.682941:0.530859:0.682941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la ecuación vectorial de la recta que :@0.616419:0.699841:0.907645:0.699841:0.907645:0.683452:0.616419:0.683452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pasa por dichos puntos.:@0.559348:0.716438:0.734391:0.716438:0.734391:0.700049:0.559348:0.700049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b) Halla:@0.530866:0.818404:0.599933:0.818404:0.599933:0.801503:0.530866:0.801503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas de la ecua-:@0.599933:0.818404:0.903637:0.818404:0.903637:0.802015:0.599933:0.802015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ción vectorial anterior.:@0.559355:0.835000:0.721610:0.835000:0.721610:0.818611:0.559355:0.818611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.072616:0.145810:0.086842:0.145810:0.086842:0.128910:0.072616:0.128910:0.000000:0.000000 Sea la ecuación vectorial = (2, 5, –3), :@0.086842:0.145810:0.392077:0.145810:0.392077:0.129422:0.086842:0.129422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.288440:0.145810:0.295903:0.145810:0.295903:0.129449:0.288440:0.129449:0.000000 t:@0.317373:0.145810:0.322754:0.145810:0.322754:0.129449:0.317373:0.129449:0.000000 encuentra:@0.392890:0.145810:0.473877:0.145810:0.473877:0.128910:0.392890:0.128910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.101107:0.162407:0.309132:0.162407:0.309132:0.146018:0.101107:0.146018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2.:@0.072616:0.273281:0.086842:0.273281:0.086842:0.256380:0.072616:0.256380:0.000000:0.000000 Sea la ecuación vectorial :@0.086842:0.273281:0.285160:0.273281:0.285160:0.256892:0.086842:0.256892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.285160:0.273281:0.292623:0.273281:0.292623:0.256919:0.285160:0.256919:0.000000 = (3, 2, 1) + (–4, –1, –1), :@0.292883:0.273281:0.451587:0.273281:0.451587:0.256892:0.292883:0.256892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.369065:0.273281:0.374123:0.273281:0.374123:0.256919:0.369065:0.256919:0.000000 determina :@0.101108:0.289877:0.187810:0.289877:0.187810:0.272976:0.101108:0.272976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.187810:0.289877:0.395836:0.289877:0.395836:0.273488:0.187810:0.273488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3.:@0.072616:0.400750:0.086842:0.400750:0.086842:0.383849:0.072616:0.383849:0.000000:0.000000 Sea la ecuación vectorial = (2, 1, –2), :@0.086842:0.400750:0.392077:0.400750:0.392077:0.384361:0.086842:0.384361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.288440:0.400750:0.295903:0.400750:0.295903:0.384388:0.288440:0.384388:0.000000 t:@0.317373:0.400750:0.322754:0.400750:0.322754:0.384388:0.317373:0.384388:0.000000 encuentra :@0.392890:0.400750:0.477692:0.400750:0.477692:0.383849:0.392890:0.383849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.101107:0.417346:0.309132:0.417346:0.309132:0.400957:0.101107:0.400957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4.:@0.072616:0.528220:0.086842:0.528220:0.086842:0.511319:0.072616:0.511319:0.000000:0.000000 Sea la ecuación vectorial = (0, 1, 3) + (4, –2, –1), :@0.086842:0.528220:0.458367:0.528220:0.458367:0.511831:0.086842:0.511831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.285160:0.528220:0.292623:0.528220:0.292623:0.511859:0.285160:0.511859:0.000000 t:@0.376843:0.528220:0.382224:0.528220:0.382224:0.511859:0.376843:0.511859:0.000000 halla :@0.101110:0.544816:0.143659:0.544816:0.143659:0.527916:0.101110:0.527916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.143659:0.544816:0.351687:0.544816:0.351687:0.528427:0.143659:0.528427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 .:@0.072616:0.655689:0.090656:0.655689:0.090656:0.638788:0.072616:0.638788:0.000000:0.000000:0.000000 Sea la ecuación vectorial = (1, 0, 0) + (–1, –2, –3), :@0.090656:0.655689:0.461683:0.655689:0.461683:0.639300:0.090656:0.639300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.285160:0.655689:0.292623:0.655689:0.292623:0.639327:0.285160:0.639327:0.000000 t:@0.373894:0.655689:0.379275:0.655689:0.379275:0.639327:0.373894:0.639327:0.000000 escribe :@0.101110:0.672285:0.161958:0.672285:0.161958:0.655384:0.101110:0.655384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.161958:0.672285:0.369984:0.672285:0.369984:0.655896:0.161958:0.655896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6 .:@0.072616:0.800979:0.090656:0.800979:0.090656:0.784078:0.072616:0.784078:0.000000:0.000000:0.000000 Sea la ecuación vectorial = (0, 2, –4), :@0.090656:0.800979:0.392278:0.800979:0.392278:0.784590:0.090656:0.784590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.288553:0.800979:0.296016:0.800979:0.296016:0.784617:0.288553:0.784617:0.000000 t:@0.317517:0.800979:0.322898:0.800979:0.322898:0.784617:0.317517:0.784617:0.000000 escribe :@0.393126:0.800979:0.453974:0.800979:0.453974:0.784078:0.393126:0.784078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las :@0.454730:0.800979:0.477912:0.800979:0.477912:0.784590:0.454730:0.784590:0.000000:0.000000:0.000000:0.000000 ecuaciones paramétricas.:@0.101103:0.817575:0.285947:0.817575:0.285947:0.801186:0.101103:0.801186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000