Answer
a) $v \cdot w=0$
b) $90^{\circ}$.
c) Orthogonal
Work Step by Step
a)
Let us consider two vectors $v=pi+qj$ and $w=xi+yj$
Then we have: $v \cdot w=(pi+qj) \cdot (xi+yj) =px+qy$
In our case, we have:
$v \cdot w=(2i +j) \cdot (i-2j) = (2)(1) +(1)(-2) \\=0$
b) and c)
We know that when the dot product between the two vectors is $0$, then they are perpendicular or orthogonal. This means that the angle between the two vectors is $90^{\circ}$. Therefore, the angle between the two vectors $v$ and $w$ is $90^{\circ}$.