Answer
$\mathbf{v}=\mathbf{i}-2\mathbf{j}$
Work Step by Step
The vector $\mathbf{v}$ with initial point ${{P}_{1}}=\left( {{x}_{1}},{{y}_{1}} \right)$ and the terminal point ${{P}_{2}}=\left( {{x}_{2}},{{y}_{2}} \right)$ can be written as
$\mathbf{v}=\left( {{x}_{2}}-{{x}_{1}} \right)\mathbf{i}+\left( {{y}_{2}}-{{y}_{1}} \right)\mathbf{j}$
Here, $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -3,0 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( -2,-2 \right)$.
So, the vector $\mathbf{v}$ is
$\begin{align}
& \mathbf{v}=\left( {{x}_{2}}-{{x}_{1}} \right)\mathbf{i}+\left( {{y}_{2}}-{{y}_{1}} \right)\mathbf{j} \\
& =\left[ -2-\left( -3 \right) \right]\mathbf{i}+\left( -2-0 \right)\mathbf{j} \\
& =\mathbf{i}-2\mathbf{j}
\end{align}$
