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: 27


$$\theta= 120^o.$$

Work Step by Step

\begin{align*} \cos \theta &=\frac{\langle 0,1,1\rangle \cdot \langle1,-1,0\rangle}{\|\langle 0,1,1\rangle\|\|\langle 1,-1,0\rangle\|}\\ &=\frac{0-1+0}{\sqrt{0+1+1}\sqrt{1+1+0}}\\ &=\frac{-1}{\sqrt{2}\sqrt{2}}\\ &=-\frac{1}{2}. \end{align*} That is $$\theta=\cos^{-1}(-\frac{1}{2})=120^o.$$
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