but how can u find the cartesian equations of the line of intersection of the plane: 2x - y + 2z = 4 and a general horizontal plane: cz + d = 0?
is it: x = 0, y = 0, z = c ?
Nope, Actually, you can write the equation of the line as the simultaneous of 2 equations, which are 2 equations of 2 planes.
Or You can find 2 different points P and Q which lie in both planes. e.g Choose P, let x = 0, you will have y = 2z - 4 (from the 1st plane), and z = -d/c(from 2nd plane) Choose Q, let y = 0 .... you'll get the cartesian co-ordinate of Q. Then find PQ vector, and write it like r = OP + t.PQ where t is parameter, O(0,0,0).
Or It can be written like (x-xP)/(xQ-xP) = (y-yP)/(yQ-yP) = (z-zP)/(zQ-zP)