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

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.5 The Dot Product - 8.5 Assess Your Understanding - Page 636: 7


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: $v \cdot w=(i-j) \cdot (i+j) = (1)(1) +(-1)(1) \\=0$ 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 $90^{\circ}$.
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