7 Three points, \(O , A\) and \(B\), are such that \(\overrightarrow { O A } = \mathbf { i } + 3 \mathbf { j } + p \mathbf { k }\) and \(\overrightarrow { O B } = - 7 \mathbf { i } + ( 1 - p ) \mathbf { j } + p \mathbf { k }\), where \(p\) is a constant.
- Find the values of \(p\) for which \(\overrightarrow { O A }\) is perpendicular to \(\overrightarrow { O B }\).
- The magnitudes of \(\overrightarrow { O A }\) and \(\overrightarrow { O B }\) are \(a\) and \(b\) respectively. Find the value of \(p\) for which \(b ^ { 2 } = 2 a ^ { 2 }\).
- Find the unit vector in the direction of \(\overrightarrow { A B }\) when \(p = - 8\).