Prove that if a line that does not lie on a plane intersects the plane, then their point of intersection contains only one point.

It will help if you construct diagrams and restate the problem to understand what you need to prove. Refer to the figure below.

If line l does not lie on plane Ƥ but intersects plane Ƥ, then line l and plane Ƥ intersect at exactly one point.

Suppose line l does not lie on plane Ƥ but intersects plane Ƥ at two points, say, Q and R.

Line l passes through points Q and R, and so, line l lies on plane Ƥ.

However, this contradicts the assumption that line l does not lie on plane Ƥ.

Therefore, line l intersects plane Ƥ at exactly one point.