The diagram shows a prism $ABCDPQRS$ with a horizontal square base $APSD$ with sides of length $6{\text{ }}cm$. The cross-section $ABCD$ is a trapezium and is such that the vertical edges $AB$ and $DC$ are of lengths $5{\text{ }}cm$ and $2{\text{ }}cm$ respectively. Unit vectors $i$, $j$ and $k$ are parallel to $AD$, $AP$ and $AB$ respectively.
a) Express each of the vectors $\overrightarrow {CP} $ and $\overrightarrow {CQ} $ in terms of $i$, $j$ and $k$.
b) Use a scalar product to calculate angle $PCQ$.

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