Use one displacement for four vector tasks

The position vectors of A, B and C are $\mathbf a=\mathbf i-\mathbf j+2\mathbf k$, $\mathbf b=3\mathbf i+5\mathbf j-2\mathbf k$ and $\mathbf c=p\mathbf j+4\mathbf k$ respectively.

(i) Find the unit vector in the direction of $\overrightarrow{AB}$.2 marks

(ii) Find the value of p such that A, B and C are collinear.3 marks

(iii) If $p=-1$, find the position vector of D such that ABCD is a parallelogram.2 marks

(iv) If $|\overrightarrow{AC}|=3$, find the possible values of p.2 marks