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