(i)[2]
Write $\overrightarrow{CP}$ and $\overrightarrow{CQ}$ in terms of $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(ii)[4]
Calculate angle $PCQ$ using a scalar product.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts a prism $ABCDPQRS$ with a horizontal square base $APSD$ of side length $6\text{ cm}$. The cross-section $ABCD$ is a trapezium, and the vertical edges $AB$ and $DC$ measure $5\text{ cm}$ and $2\text{ cm}$ respectively. Unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $AD$, $AP$ and $AB$ respectively.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The vector $\overrightarrow{CP}$ is $-6\mathbf{i}+6\mathbf{j}-2\mathbf{k}$.” …
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