Linear Algebra - Projection of Vector

[YoshiMoshi]

Homework Statement

I feel like this is a easy question but it seems the answer key doesn't seem to be right.

So say I have 2 vectors

and I'm trying to find the projection of vector u perpendicular to the vector v

Homework Equations

The Attempt at a Solution

So I don't remember doing something like this before but I would assume that I start off by finding the projection of u in direction of v

alright so this gives me

So conceptually thinking I see that I have a vector u and a vector V|| sort of like this

So I can find the angle between u and V and I get 104.963 degrees

So to get the perpendicular component is it just

tan(theta) = (V perpendicular)/(V parallel)
so V perpendicular is
(V parallel)tan(theta) = V perpendicular?

I think is conceptually ok but I'm not sure because my answer key does V - V parallel which would appear to be wrong in my opinion because I don't see how that would give us V perpendicular, unless I'm not understanding what vector I'm looking for.

Thanks for any help.

 

[YoshiMoshi]

I see that apparently the answer key is correct and see why never mind