Answer
See below:
Work Step by Step
The magnitude of a vector $\mathbf{v}=\text{a}\mathbf{i}\text{+b}\mathbf{j}$ can be given as
$\text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ }\mathbf{v}\text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ }=\sqrt{{{a}^{2}}+{{b}^{2}}}$
Comparing the above vector with the provided vector $\mathbf{v}=\text{3}\mathbf{i}\text{+}\mathbf{j}$.
$ a=3,b=1$
Substituting the values of a and b, we get
$\begin{align}
& ||\mathbf{v}||=\sqrt{{{3}^{2}}+{{1}^{2}}} \\
& ||\mathbf{v}||=\sqrt{10}
\end{align}$
The magnitude of the given vector is $||\mathbf{v}||=\sqrt{10}$.
