Use a diagonal direction for a line and a parallelogram area

Relative to O, A,B,C have position vectors $\mathbf i+6\mathbf j-2\mathbf k$, $-3\mathbf i+2\mathbf j-5\mathbf k$, $3\mathbf i-2\mathbf j+2\mathbf k$. L passes through A,C.

(i) Find a vector equation of L.2 marks

(ii) Find the exact length of projection of AB onto L.3 marks

(iii) Hence or otherwise find the shortest distance from B to L in exact form.2 marks

D is such that ABCD is a parallelogram. Use a vector product to find its exact area.3 marks