Hi, can anyone explain to me why the equation for a plane3 which contains the intersection line of 2 other planes(plane1 and plane2), is the sum of the equations of plane 1 and plane 2?

Note the planes all go through the origin.

ie, if plane 1 is ax+by+cz=0 and if plane 2 is dx+ey+fz=0

any plane containing the intersecting lines of plane 1 and plane 2 is:

(a+d)x + (b+e)y + (c+f)z = 0

Why?