Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 9 - Polar Coordinates; Vectors - 9.4 Vectors - 9.4 Assess Your Understanding - Page 606: 51

Answer

$\frac{3}{5}i-\frac{4}{5}j.$

Work Step by Step

If $v=ai+bj$ then the unit vector $u$ in the direction of $v$ is $u=\frac{v}{||v||}$, where $||v||=\sqrt{a^2+b^2}.$ $||v||=\sqrt{3^2+(-4)^2}=\sqrt{25}=5.$ Hence $u=\frac{3i-4j}{5}=\frac{3}{5}i-\frac{4}{5}j.$
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