Vector equation of line of intersection of 2 planes – video clip

lineofintersection

How to find the vector equation of the line of intersection of two planes in two steps:

  • the direction vector of that line = cross-product of the normal vectors of the two planes
  • find a point on that line by putting x=0 in the equations of both planes and thus finding out where the line of intersection crosses the yz plane

(If it turns out that the line of intersection doesn’t cross the yz plane, put y=0 in the second step instead).