8 Relative to an origin \(O\), the point \(A\) has position vector \(4 \mathbf { i } + 7 \mathbf { j } - p \mathbf { k }\) and the point \(B\) has position vector \(8 \mathbf { i } - \mathbf { j } - p \mathbf { k }\), where \(p\) is a constant.
- Find \(\overrightarrow { O A } \cdot \overrightarrow { O B }\).
- Hence show that there are no real values of \(p\) for which \(O A\) and \(O B\) are perpendicular to each other.
- Find the values of \(p\) for which angle \(A O B = 60 ^ { \circ }\).