## Precalculus (6th Edition) Blitzer

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 $\sqrt{29}$.