How to Find the Vector Between Two Points

The vector between two points can easily be expressed using the position vectors of each point. The point $P=\left(x_1,y_1\right)$ can be rewritten as a position vector: $\overrightarrow{OP}=\left(x_1,y_1\right)$.

You do the same with the other point $Q=\left(x_2,y_2\right)$, and get $\overrightarrow{OQ}=\left(x_2,y_2\right)$. You can now create the vector between the two points by subtracting the end point from the starting point, which is the difference $\overrightarrow{OQ}-\overrightarrow{OP}$. This is how you find the vector between two points: