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 235: 18


$c=\pm \frac{1}{\sqrt{14}}$.

Work Step by Step

Since $\|c(1,2,3)\|=1$ and $c(1,2,3)=(c,2c,3c)$, we have $$\sqrt{c^2+4c^2+9c^2}=1 \Longrightarrow 14 c^2=1.$$ Hence, $c=\pm \frac{1}{\sqrt{14}}$.
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