Distinguish four independent parameter cases

Relative to O, A and B have position vectors $2\mathbf i+\mathbf j+2\mathbf k$ and $3\mathbf i-2\mathbf j+p\mathbf k$, where p is a constant.

(a) Find p for which OA and OB are perpendicular.2 marks

(b) In the case p=6, find angle AOB to the nearest degree.3 marks

(c) In the case p=5, find the position vector of M on segment AB such that AM:MB=1:2.2 marks

(d) Find the values of p for which the length of AB is $\sqrt{11}$ units.4 marks