(i)[3]
Write both $\overrightarrow{PQ}$ and $\overrightarrow{RQ}$ in component form using $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(ii)[4]
Find angle $RQP$ using a scalar product.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram shows $OABCDEFG$ as a rectangular block with $OA = OD = 6$ cm and $AB = 12$ cm. The unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ run parallel to $OA$, $OC$ and $OD$ respectively. Point $P$ is the midpoint of $DG$, $Q$ is at the centre of the square face $CBFG$, and $R$ is located on $AB$ so that $AR = 4$ cm.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate vector $ \overrightarrow{PQ}=3\mathbf{i}+6\mathbf{j}-3\mathbf{k}$” …
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