If $u_1$ and $u_2$ are orthogonal unit vectors, and $v= au_1 + bu_2 $, find $ v \cdot u_1 $

Question

If $u_1$ and $u_2$ are orthogonal unit vectors, and $v= au_1 + bu_2$, find $ v.u_1 $

I understand that the dot product of $v$ and $u_1$ is $|v||u_1| \cos \theta $

I also understand that orthogonal unit vectors means $\theta = \pi/2$ means that the the dot product of $u_1$ and $u_2$ is $0$

But, ultimately I do not understand this vector question

Answer 1

Distribute the dot product: $$v\cdot u_1=a(u_1\cdot u_1)+b(u_2\cdot u_1)$$ Now use the given orthonormality of $u_1$ and $u_2$: $$=a(1)+b(0)=a$$