Unidad 3. Espacios Vectoriales Básicos 3.4 Producto escalar, vectorial y triple producto escalar Triple Producto Escalar

Description
Dados tres vectores de R 3 u = (a, b, c) v = (r, s, t) w = (x, y, z) con ellos se busca el de formar primero el producto vectorial y luego el producto punto de u con v × w. Hay una forma sencilla de obtener el resultado de este triple producto

Please download to get full document.

View again

of 3
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Information
Category:

Spiritual/ Inspirational

Publish on:

Views: 0 | Pages: 3

Extension: PDF | Download: 0

Share
Tags
Transcript
  ❯♥✐❞❛❞✸✳❊♣❛❝✐♦❱❡❝♦✐❛❧❡❇✐❝♦  ✸✳✹♦❞✉❝♦❡❝❛❧❛✱✈❡❝♦✐❛❧②✐♣❧❡♣♦❞✉❝♦❡❝❛❧❛ ❚✐♣❧❡♦❞✉❝♦❊❝❛❧❛ ❉❛❞♦❡✈❡❝♦❡❞❡  R 3 u  = ( a,b,c )  v  = ( r,s,t )  w  = ( x,y,z ) ❝♦♥❡❧❧♦❡❜✉❝❛❡❧❞❡❢♦♠❛♣✐♠❡♦❡❧♣♦❞✉❝♦✈❡❝♦✐❛❧②❧✉❡❣♦❡❧♣♦❞✉❝♦♣✉♥♦❞❡  u ❝♦♥   v  × w ✳❍❛②✉♥❛❢♦♠❛❡♥❝✐❧❧❛❞❡♦❜❡♥❡❡❧❡✉❧❛❞♦❞❡❡❡✐♣❧❡♣♦❞✉❝♦❡❝❛❧❛✱❝♦♠♦❧♦♠✉❡❛❡❧❝❧❝✉❧♦ ✐❣✉✐❡♥❡✿ u · v × w  =  a  s ty z  − b  r tx z  +  c  r sx y  =  a b cr s tx y z  = [ u,v,w ] ▲❛❧✐♠❛✐❣✉❛❧❞❛❞❞❡❄♥❡✉♥❛♥♦❛❝✐♥♣❛❛❡❧✐♣❧❡♣♦❞✉❝♦❡❝❛❧❛✉❡❡✈✐❛❡❝✐❜✐♦❞♦❡❧❞❡❡♠✐✲ ♥❛♥❡✳ ♦♣✐❡❞❛❞✶  ❊❝❝❧✐❝♦✱❡❞❡❝✐✱♣✉❡❞❡♦♠❛❡❝♦♠♦♣✐♠❡❢❛❝♦♦♦✈❡❝♦❝♦♥❛❧❞❡✉❡♥♦❡ ❛❧❡❡❡❧♦❞❡♥❝❝❧✐❝♦✭❝♦❧♦✉❡❧♦❡✈❡❝♦❡❡♥✉♥❛❝✐❝✉♥❢❡❡♥❝✐❛❝✉②♦❡❝♦✐❞♦♣❛❡♣✐♠❡♦ ♣♦  u ✱❧✉❡❣♦♣♦   v ②❄♥❛❧♠❡♥❡♣♦   w ✮❀❡♥♠❜♦❧♦  [ u,v,w ] = [ v,w,u ] = [ w,u,v ] ❉❡♠♦❛❝✐♥✳  ❊♥❡❡❝❛♦  [ u,v,w ] =  a b cr s tx y z  = 2 csx  +  cry  +  btx  + 2 brz  + 2 aty  +  asz [ v,w,u ] =  r s tx y za b c  = 2 csx  +  cry  +  btx  + 2 brz  + 2 aty  +  asz [ w,u,v ] =  x y za b cr s t  = 2 csx  +  cry  +  btx  + 2 brz  + 2 aty  +  asz ♦♣✐❡❞❛❞✷  ❈❛♠❜✐❛❞❡✐❣♥♦❛❧✐♥❡❝❛♠❜✐❛❞♦❞❡❧♦✈❡❝♦❡✭♥♦❡✉❡❡♦❝❛♠❜✐❛❡❧♦❞❡♥❝❝❧✐❝♦✮❀♣♦❡❥❡♠♣❧♦✱ [ u,v,w ] =  − [ v,u,w ] ❊♥❡❡❝❛♦  − [ v,u,w ] =  − v · u × w  =  v · w × u  = [ v,w,u ] = [ u,v,w ] ♦♣✐❡❞❛❞✸  ❙❡❞✐✐❜✉②❡♦❜❡❧❛✉♠❛✱❡❞❡❝✐✱ [ u 1  +  u 2 ,v,w ] = [ u 1 ,v,w ] + [ u 2 ,v,w ] ❋❛❝✉❧❛❞❞❡❈✐❡♥❝✐❛❯◆❆▼ ●❡♦♠❡❛❆♥❛❧✐❝❛■ ♦❢✳❊❡❜❛♥❘✉❜♥❍✉❛❞♦❈✉③  ✶   ❯♥✐❞❛❞✸✳❊♣❛❝✐♦❱❡❝♦✐❛❧❡❇✐❝♦  ✸✳✹♦❞✉❝♦❡❝❛❧❛✱✈❡❝♦✐❛❧②✐♣❧❡♣♦❞✉❝♦❡❝❛❧❛  ❉❡♠♦❛❝✐♥✳  ❊♥❡❡❝❛♦✐  u 1  = ( u 1 1 ,u 1 2 ,u 1 3 ) ②   u 2  = ( u 2 1 ,u 2 2 ,u 2 3 ) ✳❊♥♦♥❝❡  [ u 1  +  u 2 ,v,w ] = ( u 1  +  u 2 ) · v × w  u 1 1  +  u 2 1  u 1 2  +  u 2 2  u 1 3  +  u 2 3 r s tx y z  =  u 1 1  u 1 2  u 1 3 r s tx y z  +  u 2 1  u 2 2  u 2 3 r s tx y z  =  u 1  · v × w  +  u 2  · v × w = [ u 1 ,v,w ] + [ u 2 ,v,w ] ♦♣✐❡❞❛❞✹  ❙❛❝❛❡❝❛❧❛❡✱❡♦❡✱ [ λu,v,w ] =  λ [ u,v,w ] ❉❡♠♦❛❝✐♥✳  ❊♥❡❡❝❛♦✐  u 1  = ( u 1 1 ,u 1 2 ,u 1 3 ) ②   λ  ∈ R ✳❊♥♦♥❝❡  [ λu 1 ,v,w ] = ( λu 1 ) · v × w  λu 1 1  λu 1 2  λu 1 3 r s tx y z  =  λ  u 1 1  u 1 2  u 1 3 r s tx y z  =  λ ( u 1  · v × w )=  λ [ u 1 ,v,w ] ♦♣✐❡❞❛❞✺  ❊①♣❡❛❡❧✈♦❧✉♠❡♥♦✐❡♥❛❞♦❞❡❧♣❛❛❧❡❧❡♣♣❡❞♦✭  u,v,w ✮❞❡❧❛❋✐❣✉❛ ❊❛♣♦♣✐❡❞❛❞❡❞❡♠✉❡❛♦♠❛♥❞♦❡♥❝✉❡♥❛❧❛✐♥❡♣❡❛❝✐♥❣❡♦♠✐❝❛❞❡❧♦♣♦❞✉❝♦ ❛♥❡✐♦❡✿ [ u,v,w ] =  u · v × w  =   u   v × w  cos  φ ❞♦♥❞❡  φ  = ∠  ( u,v × w ) ❋❛❝✉❧❛❞❞❡❈✐❡♥❝✐❛❯◆❆▼ ●❡♦♠❡❛❆♥❛❧✐❝❛■ ♦❢✳❊❡❜❛♥❘✉❜♥❍✉❛❞♦❈✉③  ✷   ❯♥✐❞❛❞✸✳❊♣❛❝✐♦❱❡❝♦✐❛❧❡❇✐❝♦  ✸✳✹♦❞✉❝♦❡❝❛❧❛✱✈❡❝♦✐❛❧②✐♣❧❡♣♦❞✉❝♦❡❝❛❧❛ ②✱❝♦♠♦  v × w ❡♣❡♣❡♥❞✐❝✉❧❛❛   v ②   w ✱❡❧♥♠❡♦    u  cos  φ ❡❧❛❛❧✉❛❞❡   P  ( u,v,w ) ❡♣❡❝♦❞❡ ❧❛❜❛❡❢♦♠❛❞❛♣♦❡❧♣❛❛❧❡❧♦❣❛♠♦❞❡❡♠✐♥❛❞♦♣♦  u ②   w ✱❝✉②❛❡❛❡♣❡❝✐❛♠❡♥❡    u,v × w  ❋❛❝✉❧❛❞❞❡❈✐❡♥❝✐❛❯◆❆▼ ●❡♦♠❡❛❆♥❛❧✐❝❛■ ♦❢✳❊❡❜❛♥❘✉❜♥❍✉❛❞♦❈✉③  ✸ 
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks