79:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
Propiedades de la adición de vectores:@0.108231:0.097329:0.408906:0.097329:0.408906:0.079646:0.108231:0.079646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se verifican las siguientes propiedades::@0.108231:0.121164:0.379964:0.121164:0.379964:0.104667:0.108231:0.104667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.108231:0.145860:0.118769:0.145860:0.118769:0.129146:0.108231:0.129146:0.000000:0.000000
 :@0.118769:0.145643:0.122911:0.145643:0.122911:0.129145:0.118769:0.129145:0.000000
Conmutativa: :@0.131966:0.146105:0.241776:0.146105:0.241776:0.129159:0.131966:0.129159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo  ,:@0.241776:0.145643:0.332569:0.145643:0.332569:0.129145:0.241776:0.129145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.349138:0.146279:0.362874:0.146279:0.362874:0.129998:0.349138:0.129998:0.000000
+ =+:@0.405893:0.146279:0.466001:0.146279:0.466001:0.129998:0.405893:0.129998:0.000000:0.000000:0.000000:0.000000
uv:@0.318564:0.145758:0.343878:0.145758:0.343878:0.129290:0.318564:0.129290:0.000000:0.000000
Vu vv u:@0.365629:0.145758:0.476712:0.145758:0.476712:0.129290:0.365629:0.129290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.382794:0.145643:0.385549:0.145643:0.385549:0.129145:0.382794:0.129145:0.000000
2:@0.374737:0.147861:0.379654:0.147861:0.379654:0.138313:0.374737:0.138313:0.000000
.:@0.480592:0.145643:0.483347:0.145643:0.483347:0.129145:0.480592:0.129145:0.000000
 :@0.108232:0.170122:0.112374:0.170122:0.112374:0.153625:0.108232:0.153625:0.000000
En la figura 2.17. se muestra el resultado :@0.131968:0.170122:0.417149:0.170122:0.417149:0.153625:0.131968:0.153625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+=+:@0.434586:0.170757:0.497526:0.170757:0.497526:0.154476:0.434586:0.154476:0.000000:0.000000:0.000000
uv vu:@0.421910:0.170237:0.509008:0.170237:0.509008:0.153768:0.421910:0.153768:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.510503:0.170121:0.513258:0.170121:0.513258:0.153623:0.510503:0.153623:0.000000
ii):@0.108226:0.195294:0.123021:0.195294:0.123021:0.178579:0.108226:0.178579:0.000000:0.000000:0.000000
 :@0.123020:0.195077:0.127162:0.195077:0.127162:0.178579:0.123020:0.178579:0.000000
Asociativa::@0.131959:0.195540:0.216228:0.195540:0.216228:0.178594:0.131959:0.178594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 para todo :@0.216226:0.195077:0.294999:0.195077:0.294999:0.178579:0.216226:0.178579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.416167:0.198757:0.422542:0.198757:0.422542:0.177402:0.416167:0.177402:0.000000
) (:@0.459087:0.198757:0.487880:0.198757:0.487880:0.177402:0.459087:0.177402:0.000000:0.000000:0.000000
):@0.521763:0.198757:0.528138:0.198757:0.528138:0.177402:0.521763:0.177402:0.000000
∈:@0.347345:0.195743:0.360994:0.195743:0.360994:0.179565:0.347345:0.179565:0.000000
+:@0.403741:0.195743:0.414251:0.195743:0.414251:0.179565:0.403741:0.179565:0.000000
+:@0.434007:0.195743:0.444516:0.195743:0.444516:0.179565:0.434007:0.179565:0.000000
=:@0.468292:0.195743:0.478802:0.195743:0.478802:0.179565:0.468292:0.179565:0.000000
+:@0.499504:0.195743:0.510013:0.195743:0.510013:0.179565:0.499504:0.179565:0.000000
+:@0.529788:0.195743:0.540298:0.195743:0.540298:0.179565:0.529788:0.179565:0.000000
uv w:@0.297146:0.195225:0.343454:0.195225:0.343454:0.178861:0.297146:0.178861:0.000000:0.000000:0.000000:0.000000
V u:@0.363727:0.195225:0.401114:0.195225:0.401114:0.178861:0.363727:0.178861:0.000000:0.000000:0.000000
v w:@0.422650:0.195225:0.458142:0.195225:0.458142:0.178861:0.422650:0.178861:0.000000:0.000000:0.000000
u v:@0.487718:0.195225:0.519514:0.195225:0.519514:0.178861:0.487718:0.178861:0.000000:0.000000:0.000000
w:@0.541796:0.195225:0.553933:0.195225:0.553933:0.178861:0.541796:0.178861:0.000000
,,:@0.308330:0.195110:0.328086:0.195110:0.328086:0.178717:0.308330:0.178717:0.000000:0.000000
,:@0.380788:0.195110:0.383525:0.195110:0.383525:0.178717:0.380788:0.178717:0.000000
2:@0.372784:0.197315:0.377670:0.197315:0.377670:0.187827:0.372784:0.187827:0.000000
.:@0.553547:0.195077:0.556302:0.195077:0.556302:0.178579:0.553547:0.178579:0.000000
iii):@0.108231:0.220395:0.127284:0.220395:0.127284:0.203680:0.108231:0.203680:0.000000:0.000000:0.000000:0.000000
 Existencia de elemento neutro::@0.127284:0.220641:0.369233:0.220641:0.369233:0.203695:0.127284:0.203695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.369233:0.220395:0.373317:0.220395:0.373317:0.203680:0.369233:0.203680:0.000000
existe  0:@0.373764:0.220178:0.429742:0.220185:0.429742:0.203688:0.373764:0.203680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.433132:0.220822:0.446869:0.220822:0.446869:0.204541:0.433132:0.204541:0.000000
2:@0.455120:0.222404:0.460037:0.222404:0.460037:0.212856:0.455120:0.212856:0.000000
V:@0.446010:0.220301:0.456760:0.220301:0.456760:0.203832:0.446010:0.203832:0.000000
, tal que para todo :@0.463329:0.220185:0.599920:0.220185:0.599920:0.203688:0.463329:0.203688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.147157:0.238801:0.160893:0.238801:0.160893:0.222520:0.147157:0.222520:0.000000
2:@0.169145:0.240384:0.174062:0.240384:0.174062:0.230835:0.169145:0.230835:0.000000
uV u:@0.134121:0.238281:0.195451:0.238281:0.195451:0.221812:0.134121:0.221812:0.000000:0.000000:0.000000:0.000000
, :@0.177206:0.238165:0.184103:0.238165:0.184103:0.221667:0.177206:0.221667:0.000000:0.000000
+=+ =:@0.198919:0.238801:0.288175:0.238801:0.288175:0.222520:0.198919:0.222520:0.000000:0.000000:0.000000:0.000000:0.000000
00:@0.212790:0.238165:0.248257:0.238165:0.248257:0.221667:0.212790:0.221667:0.000000:0.000000
u u:@0.264151:0.238281:0.300466:0.238281:0.300466:0.221812:0.264151:0.221812:0.000000:0.000000:0.000000
.:@0.304720:0.238165:0.307475:0.238165:0.307475:0.221667:0.304720:0.221667:0.000000
iv):@0.108234:0.262861:0.127037:0.262861:0.127037:0.246146:0.108234:0.246146:0.000000:0.000000:0.000000
 :@0.127036:0.262643:0.131178:0.262643:0.131178:0.246146:0.127036:0.246146:0.000000
Existencia de opuestos aditivos: :@0.131968:0.263106:0.377823:0.263106:0.377823:0.246160:0.131968:0.246160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para cada :@0.377977:0.262643:0.451222:0.262643:0.451222:0.246146:0.377977:0.246146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.466597:0.263279:0.480333:0.263279:0.480333:0.246999:0.466597:0.246999:0.000000
2:@0.488584:0.264862:0.493502:0.264862:0.493502:0.255313:0.488584:0.255313:0.000000
uV:@0.453562:0.262759:0.490224:0.262759:0.490224:0.246290:0.453562:0.246290:0.000000:0.000000
, existe :@0.496647:0.262643:0.547621:0.262643:0.547621:0.246146:0.496647:0.246146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.562804:0.263279:0.576540:0.263279:0.576540:0.246999:0.562804:0.246999:0.000000
2:@0.584792:0.264862:0.589709:0.264862:0.589709:0.255313:0.584792:0.255313:0.000000
vV:@0.550188:0.262759:0.586426:0.262759:0.586426:0.246290:0.550188:0.246290:0.000000:0.000000
, :@0.593011:0.262643:0.599908:0.262643:0.599908:0.246146:0.593011:0.246146:0.000000:0.000000
tal que :@0.131974:0.280616:0.185261:0.280616:0.185261:0.264118:0.131974:0.264118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+=+ =:@0.200076:0.281259:0.289332:0.281259:0.289332:0.264978:0.200076:0.264978:0.000000:0.000000:0.000000:0.000000:0.000000
0 .:@0.293417:0.280623:0.308634:0.280623:0.308634:0.264125:0.293417:0.264125:0.000000:0.000000:0.000000
uv vu:@0.187400:0.280738:0.274498:0.280738:0.274498:0.264270:0.187400:0.264270:0.000000:0.000000:0.000000:0.000000:0.000000
El elemento   se llama opuesto aditivo de   y se lo nota con :@0.108237:0.305102:0.549790:0.305101:0.549790:0.288603:0.108237:0.288604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.198527:0.305217:0.206310:0.305217:0.206310:0.288748:0.198527:0.288748:0.000000
u:@0.415856:0.305217:0.425064:0.305217:0.425064:0.288748:0.415856:0.288748:0.000000
−:@0.552773:0.305737:0.563350:0.305737:0.563350:0.289456:0.552773:0.289456:0.000000
v:@0.563773:0.305217:0.571557:0.305217:0.571557:0.288748:0.563773:0.288748:0.000000
.:@0.573367:0.305101:0.576122:0.305101:0.576122:0.288603:0.573367:0.288603:0.000000
Considera  ,,:@0.108226:0.329580:0.220087:0.329581:0.220087:0.313083:0.108226:0.313082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.239044:0.330217:0.252780:0.330217:0.252780:0.313936:0.239044:0.313936:0.000000
2:@0.261032:0.331800:0.265949:0.331800:0.265949:0.322251:0.261032:0.322251:0.000000
uv wV:@0.188944:0.329696:0.262678:0.329696:0.262678:0.313228:0.188944:0.313228:0.000000:0.000000:0.000000:0.000000:0.000000
, que se muestra en la figura 2.18. La suma, :@0.270559:0.329581:0.599877:0.329581:0.599877:0.313083:0.270559:0.313083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.123047:0.347568:0.083573:0.347568:0.083573:0.331287:0.123047:0.331287:0.000000
+:@0.173098:0.347568:0.133624:0.347568:0.133624:0.331287:0.173098:0.331287:0.000000
y:@0.148959:0.346931:0.156781:0.346931:0.156781:0.330434:0.148959:0.330434:0.000000
uv vw:@0.110371:0.347047:0.198182:0.347047:0.198182:0.330578:0.110371:0.330578:0.000000:0.000000:0.000000:0.000000:0.000000
 se muestra en la figura 2.19. En la figura 2.20. se muestra :@0.202045:0.346931:0.599909:0.346931:0.599909:0.330434:0.202045:0.330434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.135925:0.367846:0.142340:0.367846:0.142340:0.345867:0.135925:0.345867:0.000000
) (:@0.181583:0.367846:0.212273:0.367846:0.212273:0.345867:0.181583:0.345867:0.000000:0.000000:0.000000
):@0.248838:0.367846:0.255254:0.367846:0.255254:0.345867:0.248838:0.345867:0.000000
+:@0.123047:0.365547:0.133624:0.365547:0.133624:0.349266:0.123047:0.349266:0.000000
+:@0.155143:0.365547:0.165720:0.365547:0.165720:0.349266:0.155143:0.349266:0.000000
+:@0.225237:0.365547:0.235813:0.365547:0.235813:0.349266:0.225237:0.349266:0.000000
+:@0.257333:0.365547:0.267909:0.365547:0.267909:0.349266:0.257333:0.349266:0.000000
y:@0.194245:0.364911:0.202067:0.364911:0.202067:0.348413:0.194245:0.348413:0.000000
u:@0.110383:0.365027:0.119592:0.365027:0.119592:0.348558:0.110383:0.348558:0.000000
v w:@0.142903:0.365027:0.180239:0.365027:0.180239:0.348558:0.142903:0.348558:0.000000:0.000000:0.000000
u v:@0.212585:0.365027:0.246159:0.365027:0.246159:0.348558:0.212585:0.348558:0.000000:0.000000:0.000000
w:@0.270202:0.365027:0.282416:0.365027:0.282416:0.348558:0.270202:0.348558:0.000000
.:@0.282935:0.364911:0.285690:0.364911:0.285690:0.348413:0.282935:0.348413:0.000000
Se verifica la siguiente propiedad :@0.108238:0.390012:0.361709:0.390012:0.361709:0.373514:0.108238:0.373514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.389100:0.390654:0.399677:0.390654:0.399677:0.374373:0.389100:0.374373:0.000000
≤:@0.426957:0.390654:0.437533:0.390654:0.437533:0.374373:0.426957:0.374373:0.000000
+:@0.474388:0.390654:0.484964:0.390654:0.484964:0.374373:0.474388:0.374373:0.000000
uv:@0.376443:0.390134:0.410042:0.390134:0.410042:0.373665:0.376443:0.373665:0.000000:0.000000
u:@0.451868:0.390134:0.461077:0.390134:0.461077:0.373665:0.451868:0.373665:0.000000
v:@0.497354:0.390134:0.505137:0.390134:0.505137:0.373665:0.497354:0.373665:0.000000
, conocida :@0.518459:0.390018:0.599913:0.390018:0.599913:0.373520:0.518459:0.373520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como desigualdad triangular.:@0.108225:0.407369:0.312492:0.407369:0.312492:0.390871:0.108225:0.390871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resta de vectores:@0.108231:0.589325:0.247281:0.589325:0.247281:0.571642:0.108231:0.571642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108231:0.613623:0.188315:0.613623:0.188315:0.596677:0.108231:0.596677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,:@0.108231:0.637639:0.160365:0.637640:0.160365:0.621142:0.108231:0.621141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.176509:0.638276:0.190245:0.638276:0.190245:0.621995:0.176509:0.621995:0.000000
2:@0.198497:0.639858:0.203414:0.639858:0.203414:0.630310:0.198497:0.630310:0.000000
uv V:@0.146355:0.637755:0.200137:0.637755:0.200137:0.621286:0.146355:0.621286:0.000000:0.000000:0.000000:0.000000
. Se define el vector :@0.204009:0.637640:0.345855:0.637640:0.345855:0.621142:0.204009:0.621142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.358412:0.638276:0.368988:0.638276:0.368988:0.621995:0.358412:0.621995:0.000000
de , del siguiente modo: :@0.384959:0.637640:0.571772:0.637640:0.571772:0.621142:0.384959:0.621142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.415318:0.639858:0.420235:0.639858:0.420235:0.630310:0.415318:0.630310:0.000000
uv:@0.345742:0.637755:0.379340:0.637755:0.379340:0.621286:0.345742:0.621286:0.000000:0.000000
V:@0.406208:0.637755:0.416958:0.637755:0.416958:0.621286:0.406208:0.621286:0.000000
( ):@0.184701:0.658554:0.220111:0.658554:0.220111:0.636575:0.184701:0.636575:0.000000:0.000000:0.000000
−= +−:@0.121147:0.656255:0.202813:0.656255:0.202813:0.639974:0.121147:0.639974:0.000000:0.000000:0.000000:0.000000:0.000000
uv u:@0.108471:0.655735:0.168362:0.655735:0.168362:0.639266:0.108471:0.639266:0.000000:0.000000:0.000000:0.000000
v:@0.203233:0.655735:0.211016:0.655735:0.211016:0.639266:0.203233:0.639266:0.000000
.:@0.220538:0.655619:0.223293:0.655619:0.223293:0.639121:0.220538:0.639121:0.000000
La resta de dos vectores se define en términos de la adición de vecto-:@0.108221:0.683655:0.595684:0.683655:0.595684:0.667157:0.108221:0.667157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
res y del opuesto aditivo. Esto es, :@0.108221:0.701006:0.347159:0.701006:0.347159:0.684508:0.108221:0.684508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.362551:0.701648:0.373128:0.701648:0.373128:0.685367:0.362551:0.685367:0.000000
uv:@0.349875:0.701127:0.383473:0.701127:0.383473:0.684658:0.349875:0.684658:0.000000:0.000000
 se expresa como la suma de :@0.389616:0.701011:0.599908:0.701011:0.599908:0.684514:0.389616:0.684514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.110377:0.718478:0.119586:0.718478:0.119586:0.702009:0.110377:0.702009:0.000000
 con el opuesto aditivo :@0.123309:0.718362:0.289891:0.718362:0.289891:0.701864:0.123309:0.701864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.292876:0.718998:0.303453:0.718998:0.303453:0.702717:0.292876:0.702717:0.000000
v:@0.303877:0.718478:0.311660:0.718478:0.311660:0.702009:0.303877:0.702009:0.000000
.:@0.313376:0.718362:0.316131:0.718362:0.316131:0.701864:0.313376:0.701864:0.000000
Debido a la existencia de opuestos aditivos, para cada :@0.108240:0.746398:0.503806:0.746398:0.503806:0.729900:0.108240:0.729900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.520215:0.747041:0.533951:0.747041:0.533951:0.730760:0.520215:0.730760:0.000000
2:@0.542202:0.748624:0.547120:0.748624:0.547120:0.739075:0.542202:0.739075:0.000000
vV:@0.507598:0.746521:0.543836:0.746521:0.543836:0.730052:0.507598:0.730052:0.000000:0.000000
 existe :@0.550421:0.746405:0.599911:0.746405:0.599911:0.729907:0.550421:0.729907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−∈:@0.111215:0.765021:0.148570:0.765021:0.148570:0.748740:0.111215:0.748740:0.000000:0.000000
2:@0.156813:0.766603:0.161731:0.766603:0.161731:0.757054:0.156813:0.757054:0.000000
vV:@0.122210:0.764500:0.158448:0.764500:0.158448:0.748031:0.122210:0.748031:0.000000:0.000000
, tal que :@0.165190:0.764384:0.225374:0.764384:0.225374:0.747887:0.165190:0.747887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.252910:0.767319:0.288320:0.767319:0.288320:0.745340:0.252910:0.745340:0.000000:0.000000:0.000000
+−:@0.240031:0.765021:0.271029:0.765021:0.271029:0.748740:0.240031:0.748740:0.000000:0.000000
=:@0.291180:0.765021:0.301757:0.765021:0.301757:0.748740:0.291180:0.748740:0.000000
0 .:@0.305841:0.764384:0.320271:0.764384:0.320271:0.747887:0.305841:0.747887:0.000000:0.000000:0.000000
v:@0.227778:0.764500:0.235561:0.764500:0.235561:0.748031:0.227778:0.748031:0.000000
v:@0.271433:0.764500:0.279216:0.764500:0.279216:0.748031:0.271433:0.748031:0.000000
Sea :@0.108237:0.793056:0.136494:0.793056:0.136494:0.776559:0.108237:0.776559:0.000000:0.000000:0.000000:0.000000
∈:@0.152474:0.792435:0.166211:0.792435:0.166211:0.776154:0.152474:0.776154:0.000000
2:@0.174462:0.794017:0.179379:0.794017:0.179379:0.784469:0.174462:0.784469:0.000000
uV:@0.139439:0.791914:0.176101:0.791914:0.176101:0.775445:0.139439:0.775445:0.000000:0.000000
. Como  ,:@0.182525:0.793056:0.256323:0.791798:0.256323:0.775301:0.182525:0.776558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−∈:@0.260427:0.792435:0.299921:0.792435:0.299921:0.776154:0.260427:0.776154:0.000000:0.000000
2:@0.308171:0.794017:0.313089:0.794017:0.313089:0.784469:0.308171:0.784469:0.000000
u:@0.242313:0.791914:0.251521:0.791914:0.251521:0.775445:0.242313:0.775445:0.000000
v V:@0.273561:0.791914:0.309818:0.791914:0.309818:0.775445:0.273561:0.775445:0.000000:0.000000:0.000000
, se sigue que :@0.317235:0.793056:0.416384:0.793056:0.416384:0.776559:0.317235:0.776559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.444869:0.795991:0.480279:0.795991:0.480279:0.774012:0.444869:0.774012:0.000000:0.000000:0.000000
+−:@0.431992:0.793692:0.462989:0.793692:0.462989:0.777411:0.431992:0.777411:0.000000:0.000000
∈:@0.482717:0.793692:0.496453:0.793692:0.496453:0.777411:0.482717:0.777411:0.000000
2:@0.504707:0.795275:0.509625:0.795275:0.509625:0.785726:0.504707:0.785726:0.000000
u:@0.419322:0.793171:0.428531:0.793171:0.428531:0.776703:0.419322:0.776703:0.000000
v:@0.463401:0.793171:0.471184:0.793171:0.471184:0.776703:0.463401:0.776703:0.000000
V:@0.495593:0.793171:0.506343:0.793171:0.506343:0.776703:0.495593:0.776703:0.000000
. A este ele-:@0.512662:0.793056:0.595763:0.793056:0.595763:0.776558:0.512662:0.776558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mento se lo ha notado :@0.108226:0.810407:0.274734:0.810407:0.274734:0.793909:0.108226:0.793909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.289541:0.811043:0.300118:0.811043:0.300118:0.794762:0.289541:0.794762:0.000000
uv:@0.276871:0.810522:0.310470:0.810522:0.310470:0.794053:0.276871:0.794053:0.000000:0.000000
. En la figura 2.21. se muestran los vecto-:@0.311721:0.810407:0.595724:0.810407:0.595724:0.793909:0.311721:0.793909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
res  ,,:@0.108222:0.827757:0.165433:0.827757:0.165433:0.811260:0.108222:0.811260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.169537:0.828394:0.128868:0.828394:0.128868:0.812113:0.169537:0.812113:0.000000
−:@0.220782:0.828394:0.180113:0.828394:0.180113:0.812113:0.220782:0.812113:0.000000
y:@0.196489:0.827757:0.204311:0.827757:0.204311:0.811260:0.196489:0.811260:0.000000
uv:@0.134301:0.827873:0.159615:0.827873:0.159615:0.811404:0.134301:0.811404:0.000000:0.000000
vu v:@0.182676:0.827873:0.241704:0.827873:0.241704:0.811404:0.182676:0.811404:0.000000:0.000000:0.000000:0.000000
.:@0.243199:0.827757:0.245954:0.827757:0.245954:0.811260:0.243199:0.811260:0.000000
Esta operación no cumple con las propiedades conmutativa ni aso-:@0.108226:0.855793:0.595767:0.855793:0.595767:0.839296:0.108226:0.839296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciativa. Tampoco posee elemento neutro y no cumple con la existen-:@0.108226:0.873144:0.595745:0.873144:0.595745:0.856646:0.108226:0.856646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cia de opuestos para la operación resta \–\.:@0.108226:0.890495:0.411246:0.890495:0.411246:0.873997:0.108226:0.873997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia digital:@0.684804:0.636312:0.827156:0.636312:0.827156:0.620840:0.684804:0.620840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observa:@0.685042:0.665362:0.743651:0.665362:0.743651:0.649889:0.685042:0.649889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 este video para :@0.743651:0.664939:0.849049:0.664939:0.849049:0.649876:0.743651:0.649876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocer una aplicación de los :@0.638498:0.680781:0.835276:0.680781:0.835276:0.665718:0.638498:0.665718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores::@0.638498:0.696623:0.695771:0.696623:0.695771:0.681560:0.638498:0.681560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/11m05:@0.638498:0.719924:0.736387:0.719924:0.736387:0.704610:0.638498:0.704610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.787313:0.365095:0.798794:0.365095:0.798794:0.355071:0.787313:0.355071:0.000000
 :@0.798794:0.365803:0.801675:0.365803:0.801675:0.354326:0.798794:0.354326:0.000000
Figura 2.18.:@0.801675:0.365803:0.856154:0.365803:0.856154:0.354326:0.801675:0.354326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.662664:0.329246:0.670952:0.329246:0.670952:0.314424:0.662664:0.314424:0.000000
v:@0.750672:0.321340:0.757677:0.321340:0.757677:0.306518:0.750672:0.306518:0.000000
w:@0.832139:0.318292:0.843132:0.318292:0.843132:0.303470:0.832139:0.303470:0.000000
p:@0.787313:0.588159:0.798794:0.588159:0.798794:0.578135:0.787313:0.578135:0.000000
 :@0.798794:0.588867:0.801675:0.588867:0.801675:0.577390:0.798794:0.577390:0.000000
Figura 2.19.:@0.801675:0.588867:0.856154:0.588867:0.856154:0.577390:0.801675:0.577390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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u:@0.805669:0.455867:0.813128:0.455867:0.813128:0.442527:0.805669:0.442527:0.000000
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uv:@0.744164:0.443509:0.771379:0.443509:0.771379:0.430169:0.744164:0.430169:0.000000:0.000000
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u:@0.710262:0.850154:0.718550:0.850154:0.718550:0.835332:0.710262:0.835332:0.000000
uv:@0.732581:0.869221:0.762820:0.869221:0.762820:0.854399:0.732581:0.854399:0.000000:0.000000
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v:@0.821584:0.847303:0.828588:0.847303:0.828588:0.832481:0.821584:0.832481:0.000000
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u:@0.664377:0.793246:0.672665:0.793246:0.672665:0.778424:0.664377:0.778424:0.000000
v:@0.744084:0.801132:0.751089:0.801132:0.751089:0.786310:0.744084:0.786310:0.000000
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p:@0.787313:0.899109:0.798794:0.899109:0.798794:0.889084:0.787313:0.889084:0.000000
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Figura 2.21.:@0.801675:0.899816:0.856154:0.899816:0.856154:0.888340:0.801675:0.888340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.787313:0.235112:0.798794:0.235112:0.798794:0.225087:0.787313:0.225087:0.000000
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Figura 2.17.:@0.801675:0.235819:0.856154:0.235819:0.856154:0.224343:0.801675:0.224343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.714206:0.216642:0.722494:0.216642:0.722494:0.201820:0.714206:0.201820:0.000000
u:@0.757146:0.101020:0.765433:0.101020:0.765433:0.086199:0.757146:0.086199:0.000000
v:@0.818138:0.156865:0.825143:0.156865:0.825143:0.142043:0.818138:0.142043:0.000000
v:@0.661030:0.155607:0.668035:0.155607:0.668035:0.140786:0.661030:0.140786:0.000000
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uv:@0.736523:0.171121:0.766762:0.171121:0.766762:0.156299:0.736523:0.156299:0.000000:0.000000
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w:@0.278901:0.496215:0.288795:0.496215:0.288795:0.482875:0.278901:0.482875:0.000000
w:@0.133238:0.496215:0.143131:0.496215:0.143131:0.482875:0.133238:0.482875:0.000000
vw:@0.222129:0.501561:0.252372:0.501561:0.252372:0.488221:0.222129:0.488221:0.000000:0.000000
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u:@0.172056:0.490566:0.179516:0.490566:0.179516:0.477226:0.172056:0.477226:0.000000
u:@0.392994:0.479019:0.400453:0.479019:0.400453:0.465679:0.392994:0.465679:0.000000
u:@0.221908:0.465160:0.229367:0.465160:0.229367:0.451820:0.221908:0.451820:0.000000
v w:@0.248249:0.465160:0.278491:0.465160:0.278491:0.451820:0.248249:0.451820:0.000000:0.000000:0.000000
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+:@0.258168:0.465581:0.266735:0.465581:0.266735:0.452394:0.258168:0.452394:0.000000
w:@0.418430:0.489742:0.428324:0.489742:0.428324:0.476403:0.418430:0.476403:0.000000
u:@0.528557:0.491026:0.536017:0.491026:0.536017:0.477686:0.528557:0.477686:0.000000
v:@0.398782:0.517526:0.405086:0.517526:0.405086:0.504187:0.398782:0.504187:0.000000
uv:@0.472211:0.480403:0.499426:0.480403:0.499426:0.467064:0.472211:0.467064:0.000000:0.000000
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uv:@0.447988:0.517626:0.475203:0.517626:0.475203:0.504286:0.447988:0.504286:0.000000:0.000000
w:@0.494678:0.517626:0.504572:0.517626:0.504572:0.504286:0.494678:0.504286:0.000000
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+:@0.458251:0.518047:0.466818:0.518047:0.466818:0.504860:0.458251:0.504860:0.000000
+:@0.484249:0.518047:0.492816:0.518047:0.492816:0.504860:0.484249:0.504860:0.000000
p:@0.526926:0.550881:0.538406:0.550881:0.538406:0.540857:0.526926:0.540857:0.000000
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Figura 2.20.:@0.541288:0.551589:0.595766:0.551589:0.595766:0.540113:0.541288:0.540113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000