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: 25



Work Step by Step

\begin{align*} \cos \theta &=\frac{\langle 1,1,1\rangle \cdot \langle 1,0,1\rangle}{\|\langle 1,1,1\rangle\|\|\langle 1,0,1\rangle\|}\\ &=\frac{1+0+1}{\sqrt{1+1+1}\sqrt{1+0+1}}\\ &=\frac{2}{\sqrt{3}\sqrt{2}}\\ &=\frac{2}{\sqrt{6}}=0.816 \end{align*} That is $$\theta=\cos^{-1}0.816=35.26^o.$$
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