10 Relative to an origin \(O\), the position vectors of points \(A\) and \(B\) are \(2 \mathbf { i } + \mathbf { j } + 2 \mathbf { k }\) and \(3 \mathbf { i } - 2 \mathbf { j } + p \mathbf { k }\) respectively.
- Find the value of \(p\) for which \(O A\) and \(O B\) are perpendicular.
- In the case where \(p = 6\), use a scalar product to find angle \(A O B\), correct to the nearest degree.
- Express the vector \(\overrightarrow { A B }\) is terms of \(p\) and hence find the values of \(p\) for which the length of \(A B\) is 3.5 units.