Answer
Two vectors are said to be equal if they have same magnitude as well as same direction.
Work Step by Step
The magnitude of $\mathbf{u}$ is
$\begin{align}
& \left\| \mathbf{u} \right\|=\sqrt{{{\left( 1-0 \right)}^{2}}+{{\left( 2-0 \right)}^{2}}} \\
& =\sqrt{1+4} \\
& =\sqrt{5}
\end{align}$
The magnitude of $\mathbf{v}$ is
$\begin{align}
& \left\| \mathbf{v} \right\|=\sqrt{{{\left( 3-2 \right)}^{2}}+{{\left( 2-0 \right)}^{2}}} \\
& =\sqrt{1+4} \\
& =\sqrt{5}
\end{align}$
Both vectors have same magnitude and direction.
Hence, $\mathbf{u}=\mathbf{v}$.
