Separate plane angles, intersections and orthogonal directions

Planes $\Pi_1,\Pi_2$ are $\mathbf r\cdot(2,4,1)=10$, $\mathbf r\cdot(1,3,1)=8$.

(i) Find their acute angle.2 marks

(ii) Obtain a vector equation of their intersection line $l_1$.2 marks

Another line $l_2$ is $(x-2)/6=(7-z)/3$, y=m, where m is real.

(iii) If Π1 and l2 intersect at (6,m,5), find m.2 marks

(iv) Show l1 and l2 are perpendicular for all m.2 marks