So if you know the positions of A and B, can you get the vector that goes from A to B? Can you show that this vector would lie in the plane?
The straight line l passes through the points A and B with position vectors 7i - 3j + 6k and 10i + 3k respectively. The plane p has equation 3x - y + 2z = 8 Show that l is parallel to p.
The point C is the foot of the perpendicular from A to p. Find a vector equation for the line which passes through C and is parallel to l.