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.

1. Find the value of \(p\) for which \(\mathbf{OA}\) and \(\mathbf{OB}\) are perpendicular.
2. In the case where \(p = 6\), use a scalar product to find angle \(AOB\), correct to the nearest degree.
3. Express the vector \(\mathbf{AB}\) in terms of \(p\) and hence find the values of \(p\) for which the length of \(AB\) is 3.5 units.