Use a projection foot to find a pyramid base area

OABC is the base of a pyramid where O is the origin. E is the highest point and D lies on OB with DE perpendicular to the base. The position vectors of A,B,C,E are respectively $-7\mathbf j+\mathbf k$, $3\mathbf i-9\mathbf j+3\mathbf k$, $4\mathbf i-5\mathbf j+3\mathbf k$, and $6\mathbf i-7\mathbf j-5\mathbf k$.

(i) Find angle AOE.2 marks

(ii) Find OD, the length of the projection of OE onto OB. Hence or otherwise show that D has position vector $2\mathbf i-6\mathbf j+2\mathbf k$.4 marks

(iii) Show A,D,C are collinear.2 marks

(iv) Show OB is perpendicular to AC. Hence find the exact area of OABC in the form $m\sqrt{66}$, where m is a constant to be determined.3 marks