So, this diagram is in 2D, but in reality we would take the intersection line of the two planes and find vector perpendicular to this line on each plane. Then take the dot product of the two, right?
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This should work (up to a sign difference), but it's easier to just dot the plane normals, which you presumably have from the plane eqns.
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This illustration from CS148 might help understanding. We basically just need the angle between the ray and the surface normal.