If I have a plane $A$ defined in the form $r \cdot n = 0$ and another plane $B: z = 7$, if I substitute $z=7$ into the first plane's equation , am I finding a point that lies on both planes or is it the equation or direction of the line that the planes form when they intersect?
I know that the cross product of the normals of both planes give the direction of the intersecting line but I'm really confused. What exactly am I getting when I substitute the plane $B: z=7$ into plane $A$'s equation?
$z=7$ is a plane. $\Bbb{A}$ is also a plane.
So when you substitute $z=7$ in $\Bbb{A}$, you get the locus of all the points that are common to both the planes. i.e. a line