Precalculus (10th Edition)

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

Chapter 9 - Polar Coordinates; Vectors - 9.6 Vectors in Space - 9.6 Assess Your Understanding - Page 625: 46

Answer

$-j.$

Work Step by Step

If $v=ai+bj+ck$ and $||v||=\sqrt{a^2+b^2+c^2}$, then the unit vector $u$ in the same direction as $v$ is $u=\frac{v}{||v||}$. The magnitude of $v$ is $||v||=\sqrt{0^2+(-3)^2+0^2}\\||v||=\sqrt{0+9+0}\\||v||=\sqrt{9}=3.$ Thus the unit vector is: $u=\frac{-3j}{3}\\u=-j.$
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