Question

Find the coordinates of the tip of the position vector which is equivalent to $\overrightarrow{AB}$, where the coordinates of A and B are (3,1) and (5,0) respectively.

Answer 1

Let O be the origin and let P(x,y) be the required point. Then, P is the tip of the position vector $\overrightarrow{OP}$ of point P.

$\overrightarrow{OP}=x\hat{i}+y\hat{j}$

And, $\overrightarrow{AB}=(5-3)\hat{i}+(0-1)\hat{j}=2\hat{i}-\hat{j}$

$\overrightarrow{OP}=\overrightarrow{AB}$

$x\hat{i}+y\hat{j}=2\hat{i}-\hat{j}$

Therefore, $x=2$ and $y=-1$.