Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 785: 120


The vector is $\frac{7}{5}\mathbf{i}-\frac{21}{5}\mathbf{j}$.

Work Step by Step

The vector is $\frac{2\left( -2 \right)+4\left( -6 \right)}{{{\left\| \mathbf{w} \right\|}^{2}}}\mathbf{w}$ The magnitude of $\mathbf{w}$ is $\begin{align} & \left\| \mathbf{w} \right\|=\sqrt{{{\left( -2 \right)}^{2}}+{{\left( 6 \right)}^{2}}} \\ & =\sqrt{4+36} \\ & =\sqrt{40} \end{align}$ Substitute the value of $\left\| \mathbf{w} \right\|$ and $\mathbf{w}$ in the above equation to get $\begin{align} & \frac{2\left( -2 \right)+4\left( -6 \right)}{{{\left( \sqrt{40} \right)}^{2}}}\left( -2\mathbf{i}+6\mathbf{j} \right)=\frac{-28}{40}\left( -2\mathbf{i}+6\mathbf{j} \right) \\ & =\frac{7}{5}\mathbf{i}-\frac{21}{5}\mathbf{j} \end{align}$
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