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: 49



Work Step by Step

Solve for $||v||$ sing the formula $||v||=\sqrt{a_1^2+b_1^2}$ to obtain: $||\textbf{v}||$= $\sqrt {3^{2}+4^{2}}= \sqrt {25}$=5 Thus, the unit vector in the same direction as $\textbf{v}$ is: $u= \dfrac{v}{|\textbf{v}|}$= $\dfrac{1}{5}(3i-4j)$ = $\dfrac{3}{5}i-\dfrac{4}{5}j$.
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