$\vec{u}$ and $\vec{v}$ are orthogonal unit vectors and $\vec{w} = a\vec{u} + b\vec{v}$.
Find $\vec{w}\cdot\vec{u}$ and $\vec{w}\cdot\vec{v}$.
(Answer should be in terms of the constants $a$ and $b$)
EDIT:
Oh boy, I was completely overthinking this. It is basically a really simple algebra problem. Here, I will show you how simple it is, on the off-chance that you are as bad at math as I am.
$\vec{w}\cdot\vec{u} = (a\vec{u} + b\vec{v})\cdot\vec{u}$
$\vec{w}\cdot\vec{u} = a\vec{u}\cdot\vec{u} + b\vec{v}\cdot\vec{u}$
$\vec{w}\cdot\vec{u} = a(\vec{u}\cdot\vec{u}) + b(\vec{v}\cdot\vec{u})$
Since $\vec{u}\cdot\vec{u} = 1$ and $\vec{v}\cdot\vec{u} = 0$ because $\vec{u}$ and $\vec{v}$ are orthogonal, we get:
$\vec{w}\cdot\vec{u} = a(1) + b(0)$
$\vec{w}\cdot\vec{u} = a$
Do the same thing for $\vec{w}\cdot\vec{v}$ and you get $\vec{w}\cdot\vec{v} = b$
Hint: If $u$ and $v$ are orthogonal then $u\cdot v=0$. Since they are unit vectors, $u\cdot u=1$ and $v\cdot v=1$.