The line (l1) is parallel to the vector 4j − k and passes through the point A whose position vector is

2i + j + 4k. The variable line (l2) is parallel to the vector i − (2 sin t)j, where 0 ≤ t < 2p, and passes

through the point B whose position vector is i + 2j + 4k. The points P and Q are on (l1)

and (l2), respectively, and PQ is perpendicular to both (l1)and (l2).

(i) Find the length of PQ in terms of t.

(ii) Hence find the values of t for which (l1)and (l2)intersect.

(iii) For the case t = pi/4, find the perpendicular distance from A to the plane BPQ, giving your answer

correct to 3 decimal places. (Answer = 0.219)

I managed to do the first two parts but can someone help me how to find the parametric equation of plane BPQ, so that I can then use the distance formula to find the perpendicular distance.(No need to do the first 2 parts to be able to do the final part)