Intersection of a Plane and a Line

are used to denote separate lines
are used to denote separate Planes
There are 3 cases for possible intersection of a line and plane
1. The line is parallel and distinct from the plane - no solution
2. The line lies on the plane - the solution is the line
3. The line intersects the plane at exactly one point - the solution is the point

Plane Intersection Possibilities.png