Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.2 - Vectors - Exercises 12.2 - Page 704: 26



Work Step by Step

Formula to find the unit vector $\hat{\textbf{v}}$ is: $\hat{\textbf{v}}=\dfrac{v}{|v|}$ Given: $v=9i-2j+6k$ and $|v|=\sqrt{(9)^2+(-2)^2+(6)^2}=\sqrt{81+4+36}=\sqrt {121}=11$ Thus, $\hat{\textbf{v}}=\dfrac{9i-2j+6k}{11}=(\dfrac{9}{11},\dfrac{-2}{11},\dfrac{6}{11})$ and $v=|v|\hat{\textbf{v}}=11(\dfrac{9}{11}i-\dfrac{-2}{11}j+\dfrac{6}{11}k)$
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