Answer
a) $v \cdot w=0$
b) $90^{\circ}$
c) Orthogonal
Work Step by Step
Let us consider two vectors $v=pi+qj$ and $w=xi+yj$
Then we have the dot product:
$v \cdot w=(pi+qj) \cdot (xi+yj) =px+qy$
a)
We calculate the dot product for the given vectors as:
$v \cdot w=(i) \cdot (-3j) = (1)(0) +(0)(-3) \\=0$
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 $90^{\circ}$.
