How can planes intersect?

1 Answer
Jul 2, 2018

Two planes (in #3# dimensional space) can intersect in one of #3# ways:

  • Not at all - if they are parallel.

  • In a line.

  • In a plane - if they are coincident.


In #3# dimensional Euclidean space, two planes may intersect as follows:

  • If one plane is identical to the other except translated by some vector not in the plane, then the two planes do not intersect - they are parallel.

  • If the two planes coincide, then they intersect in a plane.

  • If neither of the above cases hold, then the planes will intersect in a line.

Note that two planes cannot intersect in one or a finite number of points.