## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

a) $v \cdot w=0$ b) $90^{\circ}$. c) Orthogonal
Let us consider two vectors $v=pi+qj$ and $w=xi+yj$. Then we have: $v \cdot w=(pi+qj) \cdot (xi+yj) =px+qy$ a) We calculate the dot product for the given vectors: $v \cdot w=(4i) \cdot (j) = (4)(0) +(0)(1) \\=0$ 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 $90^{\circ}$.