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 782: 10


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Work Step by Step

We plot the vector by joining the origin to the point $(5,-2)$. The magnitude of the linear combination of the vector is calculated from $\left\| \mathbf{v} \right\|=\sqrt{{{a}^{2}}+{{b}^{2}}}$ Here,a is the horizontal component of $\mathbf{v}$ and b is the vertical component of $\mathbf{v}$. $\begin{align} & \left\| \mathbf{v} \right\|=\sqrt{{{(5)}^{2}}+{{(-2)}^{2}}} \\ & =\sqrt{25+4} \\ & =\sqrt{29} \end{align}$ Thus, the magnitude of the vector is $\sqrt{29}$.
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