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: 21



Work Step by Step

\begin{align*} \cos \theta &=\frac{\langle 1,1,0\rangle \cdot \langle 0,1,2\rangle}{\|\langle 1,1,0\rangle\|\|\langle 0,1,2\rangle\|}\\ &=\frac{0+1+0}{\sqrt{1+1+0}\sqrt{0+1+4}}\\ &=\frac{1}{\sqrt{2}\sqrt{5}}\\ &=\frac{1}{\sqrt{10}} \end{align*} That is $$\theta=\cos^{-1}\frac{1}{\sqrt{10}}.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.