170:@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 :@0.077739:0.090296:0.368585:0.090296:0.368585:0.064164:0.077739:0.064164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DUA:@0.769036:0.079446:0.812680:0.079446:0.812680:0.059195:0.769036:0.059195:0.000000:0.000000:0.000000 Acción y expresión:@0.716439:0.093905:0.865277:0.093905:0.865277:0.077005:0.716439:0.077005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6.:@0.502373:0.146166:0.516600:0.146166:0.516600:0.129266:0.502373:0.129266:0.000000:0.000000 Dos planos :@0.516600:0.146166:0.616645:0.146166:0.616645:0.129777:0.516600:0.129777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∏= +:@0.616695:0.145959:0.678280:0.145959:0.678280:0.129017:0.616695:0.129017:0.000000:0.000000:0.000000:0.000000 −:@0.703342:0.145959:0.713459:0.145959:0.713459:0.129017:0.703342:0.129017:0.000000 ∏= ++:@0.738631:0.145959:0.829221:0.145959:0.829221:0.129017:0.738631:0.129017:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.631668:0.148377:0.636880:0.148377:0.636880:0.138879:0.631668:0.138879:0.000000 2:@0.754271:0.148377:0.759482:0.148377:0.759482:0.138879:0.754271:0.138879:0.000000 2:@0.681297:0.146374:0.690290:0.146374:0.690290:0.129985:0.681297:0.129985:0.000000 3 son::@0.832220:0.146374:0.884553:0.146166:0.884553:0.129777:0.832220:0.129985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.656162:0.146374:0.663625:0.146374:0.663625:0.130012:0.656162:0.130012:0.000000 y:@0.691340:0.146374:0.698822:0.146374:0.698822:0.130012:0.691340:0.130012:0.000000 z:@0.717250:0.146374:0.724492:0.146374:0.724492:0.130012:0.717250:0.130012:0.000000 x:@0.780291:0.146374:0.787754:0.146374:0.787754:0.130012:0.780291:0.130012:0.000000 y:@0.807084:0.146374:0.814566:0.146374:0.814566:0.130012:0.807084:0.130012:0.000000 z:@0.841692:0.146374:0.848934:0.146374:0.848934:0.130012:0.841692:0.130012:0.000000 ; :@0.725892:0.146374:0.735843:0.146374:0.735843:0.129985:0.725892:0.129985:0.000000:0.000000 a) :@0.530871:0.169885:0.549593:0.169885:0.549593:0.152985:0.530871:0.152985:0.000000:0.000000:0.000000 Paralelos:@0.559360:0.169885:0.623654:0.169885:0.623654:0.153496:0.559360:0.153496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b) :@0.530871:0.193604:0.550902:0.193604:0.550902:0.176704:0.530871:0.176704:0.000000:0.000000:0.000000 Perpendiculares:@0.550902:0.193604:0.676816:0.193604:0.676816:0.177215:0.550902:0.177215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c) :@0.530871:0.217323:0.548506:0.217323:0.548506:0.200423:0.530871:0.200423:0.000000:0.000000:0.000000 Coincidentes:@0.548506:0.217323:0.655587:0.217323:0.655587:0.200934:0.548506:0.200934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d) :@0.530871:0.241042:0.550939:0.241042:0.550939:0.224142:0.530871:0.224142:0.000000:0.000000:0.000000 Secantes no perpendiculares:@0.550939:0.241042:0.771407:0.241042:0.771407:0.224653:0.550939:0.224653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 7.:@0.502382:0.268329:0.516608:0.268329:0.516608:0.251429:0.502382:0.251429:0.000000:0.000000 Dos vectores = (2, 1, –3) y = ( , –2, 6) son per-:@0.516608:0.268329:0.903739:0.268329:0.903739:0.251940:0.516608:0.251940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.632116:0.268329:0.641385:0.268329:0.641385:0.251968:0.632116:0.251968:0.000000 b:@0.744469:0.268329:0.753738:0.268329:0.753738:0.251968:0.744469:0.251968:0.000000 k:@0.780145:0.268329:0.787719:0.268329:0.787719:0.251968:0.780145:0.251968:0.000000 pendiculares cuando vale::@0.530871:0.284926:0.733555:0.284926:0.733555:0.268537:0.530871:0.268537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.689199:0.284926:0.696773:0.284926:0.696773:0.268565:0.689199:0.268565:0.000000 a):@0.530871:0.308645:0.545779:0.308645:0.545779:0.291744:0.530871:0.291744:0.000000:0.000000 0:@0.545779:0.308645:0.568353:0.308645:0.568353:0.292256:0.545779:0.292256:0.000000:0.000000 b):@0.637125:0.308645:0.653341:0.308645:0.653341:0.291744:0.637125:0.291744:0.000000:0.000000 –6:@0.653341:0.308645:0.683820:0.308645:0.683820:0.292256:0.653341:0.292256:0.000000:0.000000:0.000000 c):@0.743378:0.308645:0.757199:0.308645:0.757199:0.291744:0.743378:0.291744:0.000000:0.000000 6:@0.757199:0.308645:0.780860:0.308645:0.780860:0.292256:0.757199:0.292256:0.000000:0.000000 d):@0.849632:0.308645:0.865885:0.308645:0.865885:0.291744:0.849632:0.291744:0.000000:0.000000 3:@0.865885:0.308645:0.887114:0.308645:0.887114:0.292256:0.865885:0.292256:0.000000:0.000000 8.:@0.502382:0.335932:0.516608:0.335932:0.516608:0.319031:0.502382:0.319031:0.000000:0.000000 Una empresa produce dos tipos de productos: :@0.516608:0.335932:0.875650:0.335932:0.875650:0.319543:0.516608:0.319543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.875650:0.335932:0.885546:0.335932:0.885546:0.319571:0.875650:0.319571:0.000000 y . Si = unidades de e = unidades de ,:@0.530871:0.352528:0.857095:0.352528:0.857095:0.336139:0.530871:0.336139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.543015:0.352528:0.551860:0.352528:0.551860:0.336167:0.543015:0.336167:0.000000 x:@0.575539:0.352528:0.583003:0.352528:0.583003:0.336167:0.575539:0.336167:0.000000 A y:@0.696830:0.352528:0.731216:0.352528:0.731216:0.336167:0.696830:0.336167:0.000000:0.000000:0.000000 B:@0.845044:0.352528:0.853889:0.352528:0.853889:0.336167:0.845044:0.336167:0.000000 la restricción “se pueden producir máximo 100 :@0.530871:0.369125:0.873916:0.369125:0.873916:0.352736:0.530871:0.352736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 unidades en total” se expresa como::@0.530871:0.385721:0.793056:0.385721:0.793056:0.369332:0.530871:0.369332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a) :@0.530871:0.409440:0.549593:0.409440:0.549593:0.392539:0.530871:0.392539:0.000000:0.000000:0.000000 x:@0.559360:0.409440:0.566823:0.409440:0.566823:0.393079:0.559360:0.393079:0.000000 + ≥ 100:@0.566823:0.409440:0.639391:0.409440:0.639391:0.393051:0.566823:0.393051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.585877:0.409440:0.593359:0.409440:0.593359:0.393079:0.585877:0.393079:0.000000 b) :@0.530871:0.433159:0.550902:0.433159:0.550902:0.416258:0.530871:0.416258:0.000000:0.000000:0.000000 x:@0.559360:0.433159:0.566823:0.433159:0.566823:0.416798:0.559360:0.416798:0.000000 + ≤ 100:@0.566823:0.433159:0.639391:0.433159:0.639391:0.416770:0.566823:0.416770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.585877:0.433159:0.593359:0.433159:0.593359:0.416798:0.585877:0.416798:0.000000 c) :@0.743378:0.409440:0.761014:0.409440:0.761014:0.392539:0.743378:0.392539:0.000000:0.000000:0.000000 x:@0.771868:0.409440:0.779331:0.409440:0.779331:0.393079:0.771868:0.393079:0.000000 + = 100:@0.779331:0.409440:0.851899:0.409440:0.851899:0.393051:0.779331:0.393051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.798385:0.409440:0.805867:0.409440:0.805867:0.393079:0.798385:0.393079:0.000000 d) :@0.743378:0.433159:0.763446:0.433159:0.763446:0.416258:0.743378:0.416258:0.000000:0.000000:0.000000 x y:@0.771868:0.433159:0.804097:0.433159:0.804097:0.416798:0.771868:0.416798:0.000000:0.000000:0.000000 – = 100:@0.779331:0.433159:0.850130:0.433159:0.850130:0.416770:0.779331:0.416770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 9.:@0.502382:0.460446:0.516608:0.460446:0.516608:0.443546:0.502382:0.443546:0.000000:0.000000 El punto (2, 3) satisface la restricción 2 + 3 ≤ 15 :@0.516608:0.460446:0.907624:0.460446:0.907624:0.444057:0.516608:0.444057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.817586:0.460446:0.825050:0.460446:0.825050:0.444085:0.817586:0.444085:0.000000 y:@0.856082:0.460446:0.863563:0.460446:0.863563:0.444085:0.856082:0.444085:0.000000 porque::@0.530871:0.477043:0.587997:0.477043:0.587997:0.460654:0.530871:0.460654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a) :@0.530871:0.500762:0.549593:0.500762:0.549593:0.483861:0.530871:0.483861:0.000000:0.000000:0.000000 2(2) + 3(3) = 13 < 15:@0.559360:0.500762:0.707997:0.500762:0.707997:0.484373:0.559360:0.484373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b) :@0.530871:0.524481:0.550902:0.524481:0.550902:0.507580:0.530871:0.507580:0.000000:0.000000:0.000000 2(2) + 3(3) = 13 ≤ 15:@0.559360:0.524481:0.707997:0.524481:0.707997:0.508092:0.559360:0.508092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c) :@0.530871:0.548200:0.548506:0.548200:0.548506:0.531299:0.530871:0.531299:0.000000:0.000000:0.000000 2(2) + 3(3) = 13 > 15:@0.559360:0.548200:0.707997:0.548200:0.707997:0.531811:0.559360:0.531811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d) :@0.530871:0.571919:0.550939:0.571919:0.550939:0.555018:0.530871:0.555018:0.000000:0.000000:0.000000 No satisface:@0.559360:0.571919:0.646965:0.571919:0.646965:0.555530:0.559360:0.555530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 10.:@0.502382:0.599206:0.526485:0.599206:0.526485:0.582305:0.502382:0.582305:0.000000:0.000000:0.000000 En el método gráfico, la región factible es::@0.526485:0.599206:0.836217:0.599206:0.836217:0.582817:0.526485:0.582817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.661670:0.599206:0.665706:0.599206:0.665706:0.582817:0.661670:0.582817:0.000000 a) :@0.530871:0.622925:0.549593:0.622925:0.549593:0.606024:0.530871:0.606024:0.000000:0.000000:0.000000 El área donde se encuentran todas las:@0.559360:0.622925:0.836195:0.622925:0.836195:0.606536:0.559360:0.606536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 restricciones.:@0.559360:0.639521:0.654297:0.639521:0.654297:0.623132:0.559360:0.623132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b) :@0.530871:0.663240:0.550902:0.663240:0.550902:0.646339:0.530871:0.646339:0.000000:0.000000:0.000000 Solo los vértices del polígono.:@0.550902:0.663240:0.777857:0.663240:0.777857:0.646851:0.550902:0.646851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c) :@0.530871:0.686959:0.548506:0.686959:0.548506:0.670058:0.530871:0.670058:0.000000:0.000000:0.000000 La recta de la función objetivo.:@0.548506:0.686959:0.783569:0.686959:0.783569:0.670570:0.548506:0.670570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d) :@0.530871:0.710678:0.550939:0.710678:0.550939:0.693777:0.530871:0.693777:0.000000:0.000000:0.000000 El punto óptimo únicamente.:@0.550939:0.710678:0.775092:0.710678:0.775092:0.694289:0.550939:0.694289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 11.:@0.502382:0.737965:0.526485:0.737965:0.526485:0.721065:0.502382:0.721065:0.000000:0.000000:0.000000 Los vértices de una región factible son: (0,0), (0,4), :@0.526485:0.737965:0.907664:0.737965:0.907664:0.721576:0.526485:0.721576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (3,2) y (5,0). Si la función objetivo es: ( , ) = 2x + 3y, :@0.530871:0.754562:0.907698:0.754562:0.907698:0.738173:0.530871:0.738173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F x y:@0.791935:0.754562:0.826469:0.754562:0.826469:0.738200:0.791935:0.738200:0.000000:0.000000:0.000000:0.000000:0.000000 ¿cuál es el valor máximo?:@0.530871:0.771158:0.715940:0.771158:0.715940:0.754769:0.530871:0.754769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a):@0.530871:0.798445:0.545779:0.798445:0.545779:0.781545:0.530871:0.781545:0.000000:0.000000 10:@0.545779:0.798445:0.577345:0.798445:0.577345:0.782056:0.545779:0.782056:0.000000:0.000000:0.000000 b):@0.637125:0.798445:0.653341:0.798445:0.653341:0.781545:0.637125:0.781545:0.000000:0.000000 12:@0.653341:0.798445:0.683599:0.798445:0.683599:0.782056:0.653341:0.782056:0.000000:0.000000:0.000000 c):@0.743378:0.798445:0.757199:0.798445:0.757199:0.781545:0.743378:0.781545:0.000000:0.000000 15:@0.757199:0.798445:0.789853:0.798445:0.789853:0.782056:0.757199:0.782056:0.000000:0.000000:0.000000 d):@0.849632:0.798445:0.865885:0.798445:0.865885:0.781545:0.849632:0.781545:0.000000:0.000000 18:@0.865885:0.798445:0.896107:0.798445:0.896107:0.782056:0.865885:0.782056:0.000000:0.000000:0.000000 12.:@0.502382:0.825732:0.526485:0.825732:0.526485:0.808832:0.502382:0.808832:0.000000:0.000000:0.000000 Una restricción de no negatividad significa que::@0.526485:0.825732:0.878728:0.825732:0.878728:0.809344:0.526485:0.809344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.821731:0.825732:0.825767:0.825732:0.825767:0.809344:0.821731:0.809344:0.000000 a) :@0.530871:0.853020:0.549593:0.853020:0.549593:0.836119:0.530871:0.836119:0.000000:0.000000:0.000000 x:@0.559360:0.853020:0.566823:0.853020:0.566823:0.836658:0.559360:0.836658:0.000000 ≥ 0, ≥ 0:@0.566823:0.853020:0.637641:0.853020:0.637641:0.836631:0.566823:0.836631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.602112:0.853020:0.609594:0.853020:0.609594:0.836658:0.602112:0.836658:0.000000 b) :@0.530871:0.876739:0.550902:0.876739:0.550902:0.859838:0.530871:0.859838:0.000000:0.000000:0.000000 x:@0.559360:0.876739:0.566823:0.876739:0.566823:0.860377:0.559360:0.860377:0.000000 ≤ 0, ≤ 0:@0.566823:0.876739:0.637641:0.876739:0.637641:0.860350:0.566823:0.860350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.602112:0.876739:0.609594:0.876739:0.609594:0.860377:0.602112:0.860377:0.000000 c) :@0.530871:0.900458:0.548506:0.900458:0.548506:0.883557:0.530871:0.883557:0.000000:0.000000:0.000000 x:@0.559360:0.900458:0.566823:0.900458:0.566823:0.884096:0.559360:0.884096:0.000000 > 0, > 0:@0.566823:0.900458:0.637641:0.900458:0.637641:0.884069:0.566823:0.884069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.602112:0.900458:0.609594:0.900458:0.609594:0.884096:0.602112:0.884096:0.000000 d) :@0.530871:0.924177:0.550939:0.924177:0.550939:0.907276:0.530871:0.907276:0.000000:0.000000:0.000000 x:@0.559360:0.924177:0.566823:0.924177:0.566823:0.907815:0.559360:0.907815:0.000000 + ≥ 0:@0.566823:0.924177:0.621406:0.924177:0.621406:0.907788:0.566823:0.907788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.585877:0.924177:0.593359:0.924177:0.593359:0.907815:0.585877:0.907815:0.000000 Para cada una de las siguientes preguntas, :@0.072612:0.144852:0.385398:0.144852:0.385398:0.128463:0.072612:0.128463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 resuelve:@0.385398:0.144852:0.452345:0.144852:0.452345:0.127952:0.385398:0.127952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.072612:0.161449:0.084756:0.161449:0.084756:0.145060:0.072612:0.145060:0.000000:0.000000 selecciona:@0.084756:0.161449:0.167587:0.161449:0.167587:0.144548:0.084756:0.144548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la respuesta correcta.:@0.167587:0.161449:0.326284:0.161449:0.326284:0.145060:0.167587:0.145060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.072612:0.188805:0.086839:0.188805:0.086839:0.171904:0.072612:0.171904:0.000000:0.000000 Dados los vectores: :@0.086839:0.188805:0.247015:0.188805:0.247015:0.172416:0.086839:0.172416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.248243:0.188950:0.257567:0.188950:0.257567:0.172588:0.248243:0.172588:0.000000 v:@0.346554:0.188950:0.354294:0.188950:0.354294:0.172588:0.346554:0.172588:0.000000 :@0.249551:0.177719:0.159108:0.177719:0.159108:0.160971:0.249551:0.160971:0.000000 :@0.347549:0.177719:0.257107:0.177719:0.257107:0.160971:0.347549:0.160971:0.000000 =:@0.261898:0.188535:0.272015:0.188535:0.272015:0.171593:0.261898:0.171593:0.000000 −:@0.294773:0.188535:0.304889:0.188535:0.304889:0.171593:0.294773:0.171593:0.000000 =:@0.359638:0.188535:0.369755:0.188535:0.369755:0.171593:0.359638:0.171593:0.000000 −:@0.403662:0.188535:0.413778:0.188535:0.413778:0.171593:0.403662:0.171593:0.000000 (,21:@0.275239:0.188950:0.313808:0.188950:0.313808:0.172561:0.275239:0.172561:0.000000:0.000000:0.000000:0.000000 ,) y :@0.310897:0.188950:0.346223:0.188950:0.346223:0.172561:0.310897:0.172561:0.000000:0.000000:0.000000:0.000000:0.000000 (, ,42:@0.372980:0.188950:0.422697:0.188950:0.422697:0.172561:0.372980:0.172561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ), ¿cuál :@0.422660:0.188950:0.477915:0.188911:0.477915:0.172522:0.422660:0.172561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.315964:0.188950:0.324957:0.188950:0.324957:0.172561:0.315964:0.172561:0.000000 1:@0.377052:0.188950:0.386045:0.188950:0.386045:0.172561:0.377052:0.172561:0.000000 es el producto escolar de: . ?:@0.101107:0.205507:0.319767:0.205507:0.319767:0.189118:0.101107:0.189118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.292476:0.205507:0.312746:0.205507:0.312746:0.189146:0.292476:0.189146:0.000000:0.000000:0.000000 a):@0.101108:0.273611:0.116016:0.273611:0.116016:0.256711:0.101108:0.256711:0.000000:0.000000 6 :@0.116016:0.273611:0.146665:0.273611:0.146665:0.257222:0.116016:0.257222:0.000000:0.000000:0.000000:0.000000:0.000000 b):@0.206164:0.273611:0.222380:0.273611:0.222380:0.256711:0.206164:0.256711:0.000000:0.000000 –8:@0.222380:0.273611:0.252860:0.273611:0.252860:0.257222:0.222380:0.257222:0.000000:0.000000:0.000000 c):@0.311238:0.273611:0.325059:0.273611:0.325059:0.256711:0.311238:0.256711:0.000000:0.000000 –4:@0.325059:0.273611:0.357934:0.273611:0.357934:0.257222:0.325059:0.257222:0.000000:0.000000:0.000000 d):@0.416294:0.273611:0.432547:0.273611:0.432547:0.256711:0.416294:0.256711:0.000000:0.000000 10:@0.432547:0.273611:0.462769:0.273611:0.462769:0.257222:0.432547:0.257222:0.000000:0.000000:0.000000 2.:@0.072600:0.304467:0.086827:0.304467:0.086827:0.287566:0.072600:0.287566:0.000000:0.000000 El módulo del vector es: :@0.086827:0.304467:0.284426:0.304467:0.284426:0.288078:0.086827:0.288078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 w:@0.286639:0.304237:0.299373:0.304237:0.299373:0.287875:0.286639:0.287875:0.000000 :@0.287782:0.293006:0.299944:0.293006:0.299944:0.276258:0.287782:0.276258:0.000000:0.000000 =:@0.304643:0.303822:0.314760:0.303822:0.314760:0.286880:0.304643:0.286880:0.000000 −:@0.337518:0.303822:0.347635:0.303822:0.347635:0.286880:0.337518:0.286880:0.000000 (,34:@0.317985:0.304237:0.356554:0.304237:0.356554:0.287848:0.317985:0.287848:0.000000:0.000000:0.000000:0.000000 ,12:@0.356775:0.304237:0.378593:0.304237:0.378593:0.287848:0.356775:0.287848:0.000000:0.000000:0.000000 ):@0.378556:0.304237:0.383440:0.304237:0.383440:0.287848:0.378556:0.287848:0.000000 a):@0.101108:0.374351:0.116016:0.374351:0.116016:0.357451:0.101108:0.357451:0.000000:0.000000 13 :@0.116016:0.374351:0.155326:0.374351:0.155326:0.357962:0.116016:0.357962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b):@0.206164:0.374351:0.222380:0.374351:0.222380:0.357451:0.206164:0.357451:0.000000:0.000000 11:@0.222380:0.374351:0.252638:0.374351:0.252638:0.357962:0.222380:0.357962:0.000000:0.000000:0.000000 c):@0.311238:0.374351:0.325059:0.374351:0.325059:0.357451:0.311238:0.357451:0.000000:0.000000 15:@0.325059:0.374351:0.357713:0.374351:0.357713:0.357962:0.325059:0.357962:0.000000:0.000000:0.000000 d):@0.416294:0.374351:0.432547:0.374351:0.432547:0.357451:0.416294:0.357451:0.000000:0.000000 169:@0.432547:0.374351:0.471761:0.374351:0.471761:0.357962:0.432547:0.357962:0.000000:0.000000:0.000000:0.000000 3.:@0.072600:0.405207:0.086827:0.405207:0.086827:0.388306:0.072600:0.388306:0.000000:0.000000 La ecuación vectorial de la recta que pasa por el :@0.086827:0.405207:0.477957:0.405207:0.477957:0.388818:0.086827:0.388818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 punto (1, 2, –1) con vector director :@0.101089:0.421872:0.364619:0.421872:0.364619:0.405483:0.101089:0.405483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.149904:0.421872:0.158676:0.421872:0.158676:0.405511:0.149904:0.405511:0.000000 v:@0.366520:0.421646:0.374259:0.421646:0.374259:0.405285:0.366520:0.405285:0.000000 :@0.367515:0.410416:0.375070:0.410416:0.375070:0.393667:0.367515:0.393667:0.000000 =:@0.379603:0.421231:0.389720:0.421231:0.389720:0.404289:0.379603:0.404289:0.000000 −:@0.412478:0.421231:0.422595:0.421231:0.422595:0.404289:0.412478:0.404289:0.000000 (,21:@0.392945:0.421646:0.431514:0.421646:0.431514:0.405257:0.392945:0.405257:0.000000:0.000000:0.000000:0.000000 ,) es: :@0.428603:0.421646:0.477923:0.421870:0.477923:0.405481:0.428603:0.405257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.433670:0.421646:0.442663:0.421646:0.442663:0.405257:0.433670:0.405257:0.000000 a) :@0.101108:0.489974:0.119830:0.489974:0.119830:0.473073:0.101108:0.473073:0.000000:0.000000:0.000000 r:@0.131088:0.489473:0.135836:0.489473:0.135836:0.474785:0.131088:0.474785:0.000000 t:@0.212403:0.489473:0.217234:0.489473:0.217234:0.474785:0.212403:0.474785:0.000000 :@0.130807:0.479379:0.137590:0.479379:0.137590:0.464342:0.130807:0.464342:0.000000 =:@0.140767:0.489101:0.149849:0.489101:0.149849:0.473890:0.140767:0.473890:0.000000 − +:@0.179262:0.489101:0.175476:0.489101:0.175476:0.473890:0.179262:0.473890:0.000000:0.000000:0.000000 −:@0.235383:0.489101:0.209971:0.489101:0.209971:0.473890:0.235383:0.473890:0.000000 (, , 1:@0.152761:0.489473:0.196355:0.489473:0.196355:0.474760:0.152761:0.474760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.194022:0.489473:0.198407:0.489473:0.198407:0.474760:0.194022:0.474760:0.000000 (, 13:@0.217862:0.489473:0.262499:0.489473:0.262499:0.474760:0.217862:0.474760:0.000000:0.000000:0.000000:0.000000:0.000000 ,):@0.249859:0.489473:0.266833:0.489473:0.266833:0.474760:0.249859:0.474760:0.000000:0.000000 12:@0.156434:0.489473:0.174517:0.489473:0.174517:0.474760:0.156434:0.474760:0.000000:0.000000 2:@0.222545:0.489473:0.230618:0.489473:0.230618:0.474760:0.222545:0.474760:0.000000 b) :@0.101108:0.513699:0.121139:0.513699:0.121139:0.496799:0.101108:0.496799:0.000000:0.000000:0.000000 r:@0.133264:0.513991:0.138553:0.513991:0.138553:0.497630:0.133264:0.497630:0.000000 t:@0.227559:0.513991:0.232940:0.513991:0.232940:0.497630:0.227559:0.497630:0.000000 :@0.132951:0.502761:0.140507:0.502761:0.140507:0.486012:0.132951:0.486012:0.000000 =:@0.144045:0.513576:0.154161:0.513576:0.154161:0.496634:0.144045:0.496634:0.000000 −:@0.176920:0.513576:0.187036:0.513576:0.187036:0.496634:0.176920:0.496634:0.000000 +:@0.214715:0.513576:0.224831:0.513576:0.224831:0.496634:0.214715:0.496634:0.000000 −:@0.263142:0.513576:0.273259:0.513576:0.273259:0.496634:0.263142:0.496634:0.000000 (,21:@0.157386:0.513991:0.195955:0.513991:0.195955:0.497602:0.157386:0.497602:0.000000:0.000000:0.000000:0.000000 ,):@0.193044:0.513991:0.211950:0.513991:0.211950:0.497602:0.193044:0.497602:0.000000:0.000000 (, ,21:@0.233621:0.513991:0.282178:0.513991:0.282178:0.497602:0.233621:0.497602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.279580:0.513991:0.284463:0.513991:0.284463:0.497602:0.279580:0.497602:0.000000 3:@0.198111:0.513991:0.207104:0.513991:0.207104:0.497602:0.198111:0.497602:0.000000 1:@0.237694:0.513991:0.246687:0.513991:0.246687:0.497602:0.237694:0.497602:0.000000 c) :@0.101108:0.537666:0.118743:0.537666:0.118743:0.520765:0.101108:0.520765:0.000000:0.000000:0.000000 r:@0.133264:0.537507:0.138553:0.537507:0.138553:0.521146:0.133264:0.521146:0.000000 :@0.132951:0.526277:0.140507:0.526277:0.140507:0.509529:0.132951:0.509529:0.000000 =:@0.144045:0.537093:0.154161:0.537093:0.154161:0.520150:0.144045:0.520150:0.000000 − +:@0.186926:0.537093:0.221127:0.537093:0.221127:0.520150:0.186926:0.520150:0.000000:0.000000:0.000000 −:@0.253357:0.537093:0.263474:0.537093:0.263474:0.520150:0.253357:0.520150:0.000000 (, , 1:@0.157405:0.537507:0.205962:0.537507:0.205962:0.521119:0.157405:0.521119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ) (, ,21:@0.203363:0.537507:0.272393:0.537507:0.272393:0.521119:0.203363:0.521119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.269795:0.537507:0.274678:0.537507:0.274678:0.521119:0.269795:0.521119:0.000000 12:@0.161477:0.537507:0.181619:0.537507:0.181619:0.521119:0.161477:0.521119:0.000000:0.000000 1:@0.227909:0.537507:0.236902:0.537507:0.236902:0.521119:0.227909:0.521119:0.000000 d) :@0.101108:0.561390:0.121176:0.561390:0.121176:0.544489:0.101108:0.544489:0.000000:0.000000:0.000000 r:@0.133264:0.561860:0.138553:0.561860:0.138553:0.545499:0.133264:0.545499:0.000000 t:@0.157405:0.561860:0.162786:0.561860:0.162786:0.545499:0.157405:0.545499:0.000000 :@0.132951:0.550630:0.140507:0.550630:0.140507:0.533881:0.132951:0.533881:0.000000 =:@0.144045:0.561445:0.154161:0.561445:0.154161:0.544503:0.144045:0.544503:0.000000 −:@0.183001:0.561445:0.193117:0.561445:0.193117:0.544503:0.183001:0.544503:0.000000 +− −:@0.220796:0.561445:0.271324:0.561445:0.271324:0.544503:0.220796:0.544503:0.000000:0.000000:0.000000:0.000000 (,21:@0.163467:0.561860:0.202036:0.561860:0.202036:0.545471:0.163467:0.545471:0.000000:0.000000:0.000000:0.000000 ,) (, 24:@0.199125:0.561860:0.294543:0.561860:0.294543:0.545471:0.199125:0.545471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,):@0.279893:0.561860:0.299961:0.561860:0.299961:0.545471:0.279893:0.545471:0.000000:0.000000 3:@0.204192:0.561860:0.213185:0.561860:0.213185:0.545471:0.204192:0.545471:0.000000 1:@0.249469:0.561860:0.258462:0.561860:0.258462:0.545471:0.249469:0.545471:0.000000 4.:@0.072616:0.590461:0.086842:0.590461:0.086842:0.573561:0.072616:0.573561:0.000000:0.000000 Las ecuaciones paramétricas de la recta que :@0.086842:0.590461:0.427254:0.590461:0.427254:0.574072:0.086842:0.574072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pasa por el punto P (1, 2, –1) con vector director :@0.101105:0.607058:0.455942:0.607058:0.455942:0.590669:0.101105:0.590669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.103464:0.623499:0.111203:0.623499:0.111203:0.607138:0.103464:0.607138:0.000000 :@0.104459:0.612269:0.112014:0.612269:0.112014:0.595521:0.104459:0.595521:0.000000 =:@0.116547:0.623084:0.126664:0.623084:0.126664:0.606142:0.116547:0.606142:0.000000 −:@0.149422:0.623084:0.159539:0.623084:0.159539:0.606142:0.149422:0.606142:0.000000 (,21:@0.129889:0.623499:0.168458:0.623499:0.168458:0.607110:0.129889:0.607110:0.000000:0.000000:0.000000:0.000000 ,) son: :@0.165546:0.623499:0.226053:0.623723:0.226053:0.607334:0.165546:0.607110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.170614:0.623499:0.179607:0.623499:0.179607:0.607110:0.170614:0.607110:0.000000 a) :@0.101108:0.712924:0.119830:0.712924:0.119830:0.696023:0.101108:0.696023:0.000000:0.000000:0.000000 x:@0.141023:0.692279:0.148486:0.692279:0.148486:0.675917:0.141023:0.675917:0.000000 t:@0.196674:0.692279:0.202055:0.692279:0.202055:0.675917:0.196674:0.675917:0.000000 y:@0.141284:0.713024:0.148765:0.713024:0.148765:0.696663:0.141284:0.696663:0.000000 t:@0.175836:0.713024:0.181217:0.713024:0.181217:0.696663:0.175836:0.696663:0.000000 z:@0.140708:0.733770:0.147950:0.733770:0.147950:0.717408:0.140708:0.717408:0.000000 t:@0.207821:0.733770:0.213202:0.733770:0.213202:0.717408:0.207821:0.717408:0.000000 =+:@0.153846:0.691864:0.185579:0.691864:0.185579:0.674922:0.153846:0.674922:0.000000:0.000000 =:@0.154109:0.712609:0.164226:0.712609:0.164226:0.695667:0.154109:0.695667:0.000000 =− +:@0.153225:0.733355:0.196733:0.733355:0.196733:0.716413:0.153225:0.716413:0.000000:0.000000:0.000000:0.000000 :@0.130552:0.693121:0.139656:0.693121:0.139656:0.676179:0.130552:0.676179:0.000000 :@0.130552:0.714967:0.139656:0.714967:0.139656:0.698025:0.130552:0.698025:0.000000 :@0.130552:0.704635:0.139656:0.704635:0.139656:0.687693:0.130552:0.687693:0.000000 :@0.130552:0.736851:0.139656:0.736851:0.139656:0.719909:0.130552:0.719909:0.000000 :@0.130552:0.728128:0.139656:0.728128:0.139656:0.711186:0.130552:0.711186:0.000000 12:@0.166361:0.692279:0.197595:0.692279:0.197595:0.675890:0.166361:0.675890:0.000000:0.000000 2:@0.167774:0.713024:0.176767:0.713024:0.176767:0.696635:0.167774:0.696635:0.000000 13:@0.177511:0.733770:0.208746:0.733770:0.208746:0.717381:0.177511:0.717381:0.000000:0.000000 b) :@0.101108:0.780578:0.121139:0.780578:0.121139:0.763677:0.101108:0.763677:0.000000:0.000000:0.000000 x:@0.140547:0.758654:0.148010:0.758654:0.148010:0.742293:0.140547:0.742293:0.000000 t:@0.196198:0.758654:0.201579:0.758654:0.201579:0.742293:0.196198:0.742293:0.000000 y:@0.140805:0.779400:0.148286:0.779400:0.148286:0.763038:0.140805:0.763038:0.000000 t:@0.191481:0.779400:0.196862:0.779400:0.196862:0.763038:0.191481:0.763038:0.000000 z:@0.140233:0.800145:0.147476:0.800145:0.147476:0.783784:0.140233:0.783784:0.000000 t:@0.195258:0.800145:0.200639:0.800145:0.200639:0.783784:0.195258:0.783784:0.000000 =+:@0.153372:0.758239:0.185105:0.758239:0.185105:0.741297:0.153372:0.741297:0.000000:0.000000 =−:@0.153630:0.778985:0.189085:0.778985:0.189085:0.762043:0.153630:0.762043:0.000000:0.000000 =−:@0.152746:0.799730:0.184478:0.799730:0.184478:0.782788:0.152746:0.782788:0.000000:0.000000 :@0.130076:0.759497:0.139180:0.759497:0.139180:0.742554:0.130076:0.742554:0.000000 :@0.130076:0.781348:0.139180:0.781348:0.139180:0.764406:0.130076:0.764406:0.000000 :@0.130076:0.771017:0.139180:0.771017:0.139180:0.754075:0.130076:0.754075:0.000000 :@0.130076:0.803242:0.139180:0.803242:0.139180:0.786300:0.130076:0.786300:0.000000 :@0.130076:0.794515:0.139180:0.794515:0.139180:0.777573:0.130076:0.777573:0.000000 12:@0.165881:0.758667:0.197116:0.758667:0.197116:0.742278:0.165881:0.742278:0.000000:0.000000 2:@0.167299:0.779400:0.176291:0.779400:0.176291:0.763011:0.167299:0.763011:0.000000 13:@0.165257:0.800145:0.196178:0.800145:0.196178:0.783756:0.165257:0.783756:0.000000:0.000000 c) :@0.313612:0.712032:0.331248:0.712032:0.331248:0.695132:0.313612:0.695132:0.000000:0.000000:0.000000 x:@0.353527:0.692041:0.360990:0.692041:0.360990:0.675680:0.353527:0.675680:0.000000 t:@0.408865:0.692041:0.414246:0.692041:0.414246:0.675680:0.408865:0.675680:0.000000 y:@0.353785:0.712787:0.361266:0.712787:0.361266:0.696425:0.353785:0.696425:0.000000 t:@0.404774:0.712787:0.410155:0.712787:0.410155:0.696425:0.404774:0.696425:0.000000 z:@0.353213:0.733532:0.360455:0.733532:0.360455:0.717171:0.353213:0.717171:0.000000 t:@0.420327:0.733532:0.425708:0.733532:0.425708:0.717171:0.420327:0.717171:0.000000 =−:@0.366352:0.691626:0.398085:0.691626:0.398085:0.674684:0.366352:0.674684:0.000000:0.000000 =+:@0.366615:0.712372:0.402070:0.712372:0.402070:0.695430:0.366615:0.695430:0.000000:0.000000 =− +:@0.365731:0.733117:0.409238:0.733117:0.409238:0.716175:0.365731:0.716175:0.000000:0.000000:0.000000:0.000000 :@0.343056:0.692883:0.352160:0.692883:0.352160:0.675941:0.343056:0.675941:0.000000 :@0.343056:0.714729:0.352160:0.714729:0.352160:0.697787:0.343056:0.697787:0.000000 :@0.343056:0.704398:0.352160:0.704398:0.352160:0.687456:0.343056:0.687456:0.000000 :@0.343056:0.736614:0.352160:0.736614:0.352160:0.719672:0.343056:0.719672:0.000000 :@0.343056:0.727891:0.352160:0.727891:0.352160:0.710948:0.343056:0.710948:0.000000 12:@0.378865:0.692041:0.409786:0.692041:0.409786:0.675652:0.378865:0.675652:0.000000:0.000000 2:@0.380279:0.712787:0.389271:0.712787:0.389271:0.696398:0.380279:0.696398:0.000000 13:@0.390015:0.733532:0.421250:0.733532:0.421250:0.717143:0.390015:0.717143:0.000000:0.000000 d) :@0.313612:0.779686:0.333680:0.779686:0.333680:0.762786:0.313612:0.762786:0.000000:0.000000:0.000000 x:@0.353679:0.758176:0.361142:0.758176:0.361142:0.741815:0.353679:0.741815:0.000000 t:@0.409331:0.758176:0.414711:0.758176:0.414711:0.741815:0.409331:0.741815:0.000000 y:@0.353937:0.778908:0.361419:0.778908:0.361419:0.762547:0.353937:0.762547:0.000000 t:@0.404613:0.778908:0.409994:0.778908:0.409994:0.762547:0.404613:0.762547:0.000000 z:@0.353366:0.799653:0.360608:0.799653:0.360608:0.783292:0.353366:0.783292:0.000000 t:@0.420479:0.799653:0.425860:0.799653:0.425860:0.783292:0.420479:0.783292:0.000000 = +:@0.366505:0.757761:0.398233:0.757761:0.398233:0.740819:0.366505:0.740819:0.000000:0.000000:0.000000 = −:@0.366763:0.778493:0.402214:0.778493:0.402214:0.761551:0.366763:0.761551:0.000000:0.000000:0.000000 = − +:@0.365860:0.799239:0.409386:0.799239:0.409386:0.782296:0.365860:0.782296:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.343194:0.759006:0.352297:0.759006:0.352297:0.742064:0.343194:0.742064:0.000000 :@0.343194:0.780858:0.352297:0.780858:0.352297:0.763916:0.343194:0.763916:0.000000 :@0.343194:0.770541:0.352297:0.770541:0.352297:0.753599:0.343194:0.753599:0.000000 :@0.343194:0.802765:0.352297:0.802765:0.352297:0.785823:0.343194:0.785823:0.000000 :@0.343194:0.794038:0.352297:0.794038:0.352297:0.777096:0.343194:0.777096:0.000000 12:@0.378999:0.758204:0.410234:0.758204:0.410234:0.741815:0.378999:0.741815:0.000000:0.000000 2:@0.380418:0.778937:0.389410:0.778937:0.389410:0.762548:0.380418:0.762548:0.000000 13:@0.390147:0.799682:0.421382:0.799682:0.421382:0.783293:0.390147:0.783293:0.000000:0.000000 5.:@0.072616:0.828026:0.086842:0.828026:0.086842:0.811125:0.072616:0.811125:0.000000:0.000000 El vector normal al plano: 3x – 2y + 5z – 7 = 0 es: :@0.086842:0.828026:0.462528:0.828026:0.462528:0.811637:0.086842:0.811637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a) :@0.101108:0.897913:0.119830:0.897913:0.119830:0.881012:0.101108:0.881012:0.000000:0.000000:0.000000 (3, –2, 5):@0.129597:0.897913:0.190040:0.897913:0.190040:0.881524:0.129597:0.881524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b) :@0.101108:0.921632:0.121139:0.921632:0.121139:0.904731:0.101108:0.904731:0.000000:0.000000:0.000000 (3, –2, –7):@0.129597:0.921632:0.199254:0.921632:0.199254:0.905243:0.129597:0.905243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c) :@0.313615:0.897913:0.331251:0.897913:0.331251:0.881012:0.313615:0.881012:0.000000:0.000000:0.000000 (1, –2, 5):@0.342105:0.897913:0.402547:0.897913:0.402547:0.881524:0.342105:0.881524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d) :@0.313615:0.921632:0.333683:0.921632:0.333683:0.904731:0.313615:0.904731:0.000000:0.000000:0.000000 (–3, 2, 7):@0.342105:0.921632:0.402547:0.921632:0.402547:0.905243:0.342105:0.905243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ref.I.M.5.7.1.:@0.072616:0.114057:0.135926:0.114057:0.135926:0.102138:0.072616:0.102138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000