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: 18



Work Step by Step

Let us consider two vectors $v=pi+qj$ and $w=xi+yj$ The dot product is given as $v \cdot w=(pi+qj) \cdot (xi+yj) =px+qy$ We know that when the dot product between two vectors is $0$, then they are perpendicular or orthogonal. This means that the angle between the two vectors is $90^{\circ}$. We have the given vectors : $v=i +j$ and $ w=i+bj$ Since, both vectors are orthogonal, then $v \cdot w=0$ $v \cdot w=(i+j) \cdot (i+bj) =0 \implies (1)(1) +(1)(b) \\=0 \\ \implies 1+b =0 \\ \implies b=-1$
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