Relative to an origin $O$, the position vectors of points $A$ and $B$ are given by
$\overrightarrow {OA} = 5i + j + 2k$ and
$\overrightarrow {OB} = 2i + 7j + pk$,
where $p$ is a constant.
a) Find the value of $p$ for which angle $AOB$ is ${90^ \circ }$.
b) In the case where $p = 4$, find the vector which has magnitude 28 and is in the same direction as $\overrightarrow {AB} $.
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