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: 26



Work Step by Step

\begin{align*} \cos \theta &=\frac{\langle 3,1,1\rangle \cdot \langle 2,-4,2\rangle}{\|\langle 3,1,1\rangle\|\|\langle 2,-4,2\rangle\|}\\ &=\frac{6-4+2}{\sqrt{9+1+1}\sqrt{4+16+4}}\\ &=\frac{4}{\sqrt{11}\sqrt{24}}\\ &=0.246. \end{align*} That is $$\theta=\cos^{-1}0.246=75.75^o.$$
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