"All limits, especially national ones, are contrary to the nature of mathematics… Mathematics knows no races… For mathematics the whole cultural world is a single country" – David Hilbert. "Face problems with a minimum of blind calculation, a maximum of seeing thought" – Hermann Minkowski

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

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).