In the diagram, $OABCDEFG$ is a rectangular block in which $OA = OD = 6{\text{ }}cm$ and $AB = 12{\text{ }}cm$. The unit vectors $i$, $j$ and $k$ are parallel to $\overrightarrow {OA} $, $\overrightarrow {OC} $ and $\overrightarrow {OD} $ respectively. The point $P$ is the mid-point of $DG$, $Q$ is the centre of the square face $CBFG$ and $R$ lies on $AB$ such that $AR = 4{\text{ }}cm$.
a) Express each of the vectors $\overrightarrow {PQ} $ and $\overrightarrow {RQ} $ in terms of $i$, $j$ and $k$.
b) Use a scalar product to find angle $RQP$.

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