Calculating Inner Products in an Inner Product Space

[FeynmanIsCool]

Homework Statement

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})

Homework Equations

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

The Attempt at a Solution

Im not sure where to start. This seems like a very simple problem, but I am confused on where to start. I can't expand inner products and solve for v,u or w since the inner product formula is not known. I also can't expand inner product(\vec{2v-w},\vec{3u+2w}) since I don't 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?
Thanks in advance!

 

[vela]

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

 

[FeynmanIsCool]

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

edit* its -101