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 - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 236: 69


orthogonal. $u\cdot v=0$.

Work Step by Step

The vectors ${u}=(\cos \theta, \sin \theta,-1), \quad {v}=(\sin \theta,-\cos \theta, 0)$ are orthogonal. Since $$u\cdot v=\cos \theta \sin \theta -\cos \theta \sin \theta+0=0,$$ then the angle between $u$ and $v$ is $\frac{\pi}{2}$.
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