- #1

mitch987

- 8

- 0

**Help!? Linear algebra proof**

## Homework Statement

Suppose that

**u,v,w**are geometric vectors such that

**u[tex]\neq[/tex]0**,

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

**u[tex]\cdot[/tex]w**and

**u**x

**v**=

**u**x

**w**

Prove that

**v**=

**w**

## Homework Equations

## 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|

**u**x

**v**=

**u**x

**w**

|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