Topics: Geometry - 3D Space - Plane - Angle


The angle between two planes and with their respective equations…

…is determined by the equality:

Given the respective normal vectors, we can rewrite this equality as:

Notice the formula is very similar to the one used to obtain the angle between lines.


  • The planes and are parallel if and only if there exists a real number such that:
  • The planes and are the same plane if they’re parallel and if .

  • The planes and are orthogonal if and only if (i.e. if ).