Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 5 - Inner Product Spaces - Review Exercises - Page 284: 12


$$\| v \| =\sqrt{5}.$$ $$\frac{1}{\| v \|}v=\frac{1}{\sqrt{5}}(0,2,-1)$$

Work Step by Step

Let $ v=(0,2,-1)$, then we have $$\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2+v_3^2 }=\sqrt{5}.$$ The unit vector in direction of $v$ is given by $$\frac{1}{\| v \|}v=\frac{1}{\sqrt{5}}(0,2,-1)$$
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