Answer
$2\sqrt{26}$
Work Step by Step
Here, $\mathbf{v}=\mathbf{i}-5\mathbf{j}$
So,
$\begin{align}
& -2\mathbf{v}=-2\left( \mathbf{i}-5\mathbf{j} \right) \\
& =-2\mathbf{i}+10\mathbf{j}
\end{align}$
The magnitude of $\mathbf{v}=a\mathbf{i}+b\mathbf{j}$ is given by $\left\| \mathbf{v} \right\|=\sqrt{{{a}^{2}}+{{b}^{2}}}$.
So, the magnitude of $-2\mathbf{v}=-2\mathbf{i}+10\mathbf{j}$ is calculated as below:
$\begin{align}
& \left\| -2\mathbf{v} \right\|=\sqrt{{{\left( -2 \right)}^{2}}+{{\left( 10 \right)}^{2}}} \\
& =\sqrt{4+100} \\
& =\sqrt{104} \\
& =2\sqrt{26}
\end{align}$
Hence, the scalar $\left\| -2\mathbf{v} \right\|=2\sqrt{26}$.
