WAEC 2022 · Paper 1 · Q21

If $\overrightarrow{PQ} = -2\mathbf{i} + 5\mathbf{j}$ and $\overrightarrow{RQ} = -\mathbf{i} - 7\mathbf{j}$ , find $\overrightarrow{PR}$ .

Worked solution (try it first)

Go from P to R through Q: $\overrightarrow{PR} = \overrightarrow{PQ} + \overrightarrow{QR}$ .
$\overrightarrow{QR}$ is $\overrightarrow{RQ}$ reversed: $\overrightarrow{QR} = \mathbf{i} + 7\mathbf{j}$ .
So $\overrightarrow{PR} = (-2 + 1)\mathbf{i} + (5 + 7)\mathbf{j}$
$= -\mathbf{i} + 12\mathbf{j}$ , option C.