Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - 8.4 - Vectors and Dot Products - 8.4 Exercises - Page 597: 91a

Answer

$u$ and $v$ have the same direction.

Work Step by Step

The angle $\theta$ between $u$ and $v$ is equal to $0$. $proj_vu=\frac{u\cdot v}{|v|^2}v=\frac{|u||v|~cos~0}{|v|^2}v=|u|\frac{v}{|v|}$ But, $\frac{v}{|v|}=\frac{u}{|u|}$ because $u$ and $v$ have the same direction ($\theta=0$). $proj_vu=|u|\frac{u}{|u|}=u$
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