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: 45



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 $||v||=\sqrt{5^2+0^2+0^2}\\ ||v||=\sqrt{25+0+0}\\ ||v||=\sqrt{25}\\ ||v||=5$ Thus the unit vector in the same direction is $v$ is: $u=\frac{5i}{5} \\u=i$
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