Prove a rhombus using a perpendicular projection

Relative to O, A,B,C have position vectors $\mathbf a=3\mathbf i-\mathbf j$, $\mathbf b=3\mathbf i+4\mathbf j-12\mathbf k$, $\mathbf c=\lambda\mathbf j+12\mathbf k$. Line $l_1$ through A,C has equation $(x-3)/3=(y+1)/4=-z/12$.

(i) Show λ=−5.2 marks

(ii) Find the position vector of P on OA with BP perpendicular to OA. Hence or otherwise prove OBAC is a rhombus.5 marks

(iii) Find the area of OBAC.2 marks

(iv) Line $l_2$ passes through O,Q, where Q lies on BA produced with BA/BQ=1/4. Find the acute angle between $l_1,l_2$.3 marks