Answer
Vector $\mathbf{v}$ with initial point ${{P}_{1}}=\left( {{x}_{1}},{{y}_{1}} \right)$ and terminal, and point ${{P}_{2}}=\left( {{x}_{2}},{{y}_{2}} \right)$ is equal to the vector: $\mathbf{v}\text{ = }\left( {{x}_{2}}-{{x}_{1}} \right)\mathbf{i}\text{ +}\left( {{y}_{2}}-{{y}_{1}} \right)\mathbf{j}$
Work Step by Step
We will consider the initial point ${{P}_{1}}=\left( {{x}_{1}},{{y}_{1}} \right)$ to final point ${{P}_{2}}=\left( {{x}_{2}},{{y}_{2}} \right)$ on Cartesian coordinates; it can be represented in vector form $\mathbf{v}$ from initial point ${{P}_{1}}=\left( {{x}_{1}},{{y}_{1}} \right)$ to final point ${{P}_{2}}=\left( {{x}_{2}},{{y}_{2}} \right)$ as:
$\mathbf{v}\text{ = }\left( {{x}_{2}}-{{x}_{1}} \right)\mathbf{i}\text{ +}\left( {{y}_{2}}-{{y}_{1}} \right)\mathbf{j}$
Then vector $\mathbf{v}$ is called a displacement vector.
