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

a) $v \cdot w=0$ b) $90^{\circ}$ c) Orthogonal
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: $v \cdot w=(i-j) \cdot (i+j) = (1)(1) +(-1)(1) \\=0$ b) and c) We know that when the dot product between the two vectors is $0$, then they are perpendicular or orthogonal to each other. This means that the angle between the two vectors is $90^{\circ}$.Therefore, the angle between the two vectors $v$ and $w$ is $90^{\circ}$.