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: 19


$\theta =\pi+2n\pi=(2n+1)\pi$, $n$ is an integer.

Work Step by Step

Let $u=(10,-5,15),\quad v=(-2,1,-3), \quad \langle u, v\rangle=u\cdot v $. The angle $\theta$ between $u$ and $v$ is given by the formula $$\cos \theta=\frac{\langle u, v\rangle}{\|u\| \cdot\|v\|}=\frac{-20-5-45}{\sqrt{ 100+25+225}\sqrt{ 4+1+9}}=\frac{-70}{\sqrt{ 4900}}=-1.$$ That is, $\theta =\pi+2n\pi=(2n+1)\pi$, $n$ is an integer.
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