(adsbygoogle = window.adsbygoogle || []).push({}); Help!? Linear algebra proof

1. The problem statement, all variables and given/known data

Suppose thatu,v,ware geometric vectors such thatu[tex]\neq[/tex]0,

u[tex]\cdot[/tex]v=u[tex]\cdot[/tex]wanduxv=uxw

Prove thatv=w

2. Relevant equations

3. The attempt at a solution

So far, I'm not sure if this is correct

u[tex]\cdot[/tex]v=u[tex]\cdot[/tex]w

|u||v|cos[tex]\theta[/tex]=|u||w|cos[tex]\theta[/tex]

|v|=|u|

uxv=uxw

|u||v|sin[tex]\theta[/tex][tex]\hat{(u\times v)}[/tex]=|u||w|sin[tex]\theta[/tex][tex]\hat{(u\times w)}[/tex]

|w|sin[tex]\theta[/tex][tex]\hat{(u\times v)}[/tex]=|w|sin[tex]\theta[/tex][tex]\hat{(u\times w)}[/tex]

[tex]\hat{(u\times v)}[/tex]=[tex]\hat{(u\times w)}[/tex]

therefore, v=w

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# Homework Help: Help? Linear algebra proof

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