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 8.4 Vectors - 8.4 Assess Your Understanding - Page 627: 50


$\dfrac{ -5}{13}i+\dfrac{ 12}{13}j$

Work Step by Step

Let us consider two vectors $v=pi+qj$ and $w=xi+yj$; then we have the unit vector $u$ in the same direction as $v$ given by: $u=\dfrac{v}{||v||}$ and the magnitude of any vector (let us say $v$) can be determined using the formula $||v||=\sqrt{p^2+q^2} $ We have: $||v||=\sqrt {(-5)^2+(12)^2}=\sqrt {169}=13$ Therefore, the unit vector $u$ in the same direction as $v$ is : $u=\dfrac{v}{||v||}=\dfrac{ -5i+12j}{13}=\dfrac{ -5}{13}i+\dfrac{ 12}{13}j$
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