# Thread: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is equal

1. ## Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is equal

Hi There

I'm really struggling with these question:

Projau = Projav is true for some vectors a, u and w.

Show: u · v = v · a
Show: counter example to show that u isnt equal to v

I seem to have these looooooooong roundabout routes that arent making sense for the first, and for the second i have no idea how to work out a counter example!

Any help would be very appreciated!

2. ## Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

Originally Posted by LucyA
Hi There

I'm really struggling with these question:

Projau = Projav is true for some vectors a, u and w.

Show: u · v = v · a
Show: counter example to show that u isnt equal to v !
Don't you mean $\large{\vec{u}\cdot\vec{a}=\vec{v}\cdot\vec{a}~?}$
Can we assume that $\text{Proj}_{\vec{a}}\vec{u}=\dfrac{\vec{u}\cdot \vec{a}}{\vec{a}\cdot \vec{a}}\vec{a}~?$

3. ## Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

thats the problem im having! but no, definitely that??? thanks so much for replying!

4. ## Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

oh gosh sorry just got informed there was an error there! however, for the second question, i have no idea how to go about counter example????

5. ## Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

Originally Posted by LucyA
oh gosh sorry just got informed there was an error there! however, for the second question, i have no idea how to go about counter example????
Consider the vectors: $\vec{a}=<1 ,1 ,0 >,~\vec{u}<1 ,1 ,\sqrt{2} >,~\&~\vec{v}<1,1,-\sqrt{2} >$

woo!