With respect to an origin O, the point A has a position vector i +3j - 4k and the point B has position vector -12i + 8j - 4k. The point P is on the line OA. The point Q and R are such that PQ = 1/3 QB and OR = 5 OQ.
I) Show that R is on the line l whose vector equation is
r = -15i + 10j + 5k + Ө (i + 3j - 4k)
II) The plane II contains the line l and is parallel to the vector 11i + 7j + 8k. The line through A perpendicular to II meets II at L, and M is such that AM = 1/5 AL. Find the position vector of M.
I know how to show R is on the line l with vector equation. But how do you do part two? HELP please!