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 - 5.2 Inner Product Spaces - 5.2 Exercises - Page 246: 44

Answer

$$\cos \theta=0.$$ That is $\theta=\frac{\pi}{2}$.

Work Step by Step

Let $u=(2,-1),\quad v=(\frac{1}{2},1), \quad =u\cdot v $The angle $\theta$ between $u$ and $v$ is given by the formula $$\cos \theta=\frac{}{\|u\| \cdot\|v\|}=\frac{1-1}{\sqrt{ 4+1}\sqrt{ \frac{1}{4}+1}}=0.$$ That is $\theta=\frac{\pi}{2}$.
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