Question

Planes A and B intersect.

Answer 1

For an analogy, imagine you have a cake with a totally flat two-dimensional surface (a plane). Imagine taking a "one-dimensional" toothpick (a line), and sticking it into the surface of the cake. Does that toothpick puncture the cake in just one spot on its surface, or along a whole line? If the line m in this diagram is your toothpick, and the plane A is your cake, where does m puncture the surface?

Answer 2

In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line:

• it is the entire line if that line is embedded in the plane,
• it is the empty set if the line is parallel to the plane but outside it.
• Otherwise, the line cuts through the plane at a single point (see attached picture for details).

In your case line m is not parallel to the plane A and is not embedded in the plane, then the intersection is the point. Since point X is common point of the line m and the plane A, then the intersection of plane A and line m is point X.

Answer: correct choice is C.