Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 666: 20



Work Step by Step

\begin{align*} \cos \theta &=\frac{\langle 1,1,1\rangle \cdot \langle 2,-1,2\rangle}{\|\langle 1,1,1\rangle\|\|\langle 2,-1,2\rangle\|}\\ &=\frac{2-1+2}{\sqrt{1+1+1}\sqrt{4+1+4}}\\ &=\frac{3}{\sqrt{3}\sqrt{9}}\\ &=\frac{1}{\sqrt{3}} \end{align*} That is $$\theta=\cos^{-1}\frac{1}{\sqrt{3}}.$$
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