Topics: Geometry - 3D Space - Plane

Given two planes in we can find the line where they intersect by:

  1. Finding their normal vectors and calculating the cross product between them
  2. Finding a common point between them (we can find such a point by giving a variable a concrete value, then solving the resulting equation system)
  3. Building a line with such a point and vector

In general, let:

…be the equations for two planes and in . Then, the intersection line for these planes is:

…where is a common point between the planes, and and are the normal vectors for each respective plane.