Answer
See below:
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 $\sqrt{29}$.
