Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 5 - Inner Product Spaces - Review Exercises - Page 284: 20


$\theta =95.73^o$.

Work Step by Step

Let $u=(1,0,-3,0),\quad v=(2,-2,1,1), \quad \langle u, v\rangle=u\cdot v $. The angle $\theta$ between $u$ and $v$ is given by the formula $$\cos \theta=\frac{\langle u, v\rangle}{\|u\| \cdot\|v\|}=\frac{2+0-3+0}{\sqrt{ 1+0+9+0}\sqrt{ 4+4+1+1}}=\frac{-1}{\sqrt{ 100}}=\frac{-1}{10}.$$ That is, $\theta =95.73^o$.
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