We want to find the component of plane A that is parallel to plane B and the component of plane A that is perpendicular to plane B.
Since the planes are infinite the projection of plane A onto plane B will be the whole of plane B.
If there is a scalar value associated with the plane then, will that value be reduced depending on the angle between the planes?
Related Question
Can we project points in the 2 dimensional coordinates of one plane into the points in the 2 dimensional coordinates of another plane?