# Inner product space vectors

1. Jul 29, 2014

### FeynmanIsCool

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

Suppose $\vec{u}$, $\vec{v}$ and $\vec{w}$ are vectors in an inner product space such that:

inner product: $\vec{u},\vec{v}= 2$
inner product: $\vec{v},\vec{w}= -6$
inner product: $\vec{u},\vec{w}= -3$

norm$(\vec{u}) = 1$
norm$(\vec{v}) = 2$
norm$(\vec{w}) = 7$

Compute:

innerproduct: ($\vec{2v-w},\vec{3u+2w}$)

2. Relevant equations

$\vec{u}$, $\vec{v}$ and $\vec{w}$$\in$Rn .The inner product type is not specified (ie. euclidean, weighted ect...)

3. The attempt at a solution

Im not sure where to start. This seems like a very simple problem, but im confused on where to start. I cant expand inner products and solve for v,u or w since the inner product formula is not known. I also cant expand inner product($\vec{2v-w},\vec{3u+2w}$) since I dont know the inner product formula. All I can think of doing right now is expanding norm$(\vec{u},\vec{v},\vec{w})$ to equal $\sqrt{innerproduct(\vec{u},\vec{u}})$, $\sqrt{innerproduct(\vec{v},\vec{v}})$, $\sqrt{innerproduct(\vec{w},\vec{w}})$ but that gets me no where as well.
Can someone give a point in the right direction?

Last edited: Jul 29, 2014
2. Jul 29, 2014

### vela

Staff Emeritus
You should look up what properties a function has to satisfy to be considered an inner product.

3. Jul 29, 2014

### FeynmanIsCool

ahh yes, the algebraic properties of inner product spaces. Of course!
Thanks

edit* its -101

Last edited: Jul 29, 2014