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: 16


$$\cos \theta=\frac{-1}{\sqrt 2}$$ That is, $\theta = 135^o$

Work Step by Step

Let $u=(1,-1),\quad v=(0,1), \quad =u\cdot v $. The angle $\theta$ between $u$ and $v$ is given by the formula $$\cos \theta=\frac{\langle u,v\rangle}{\|u\| \cdot\|v\|}=\frac{0-1}{\sqrt{ 1+1}\sqrt{ 0+1}}=\frac{-1}{\sqrt 2}$$ That is, $\theta = 135^o$
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