Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 11 - Three-Dimensional Space; Vectors - 11.2 Vectors - Exercises Set 11.2 - Page 783: 31

Answer

\[ \left\langle-\frac{2}{3}, 1\right\rangle \]

Work Step by Step

The vectors are given as: \[ \quad \vec{v}=\langle 2,1\rangle, \quad \vec{w}=\langle 4,-1\rangle, \vec{u}=\langle 1,3\rangle \] \[ -\vec{v}+\vec{x}+2 \vec{u}=\vec{w}+7 \vec{x} \] and then \[ \begin{aligned} 6 \vec{x} &=-\vec{v}-\vec{w}+2 \vec{u} \\ &=-\langle 2,1\rangle-\langle 4,-1\rangle +2\langle 1,3\rangle\\ &=\langle-2,-1\rangle+\langle-4,1\rangle +\langle 2,6\rangle\\ &=\langle-4,6\rangle \end{aligned} \] We have: \[ \vec{x}= \langle-4,6\rangle \frac{1}{6}=\left\langle-\frac{2}{3}, 1\right\rangle \]
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