Answer
See below:
Work Step by Step
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 $\mathbf{v}$.
The next step is:
$\begin{align}
& \left\| \mathbf{v} \right\|=\sqrt{{{1}^{2}}+{{(-1)}^{2}}} \\
& =\sqrt{1+1} \\
& =\sqrt{2}
\end{align}$
Thus, the magnitude of the vector is $\sqrt{2}$.
