offset $d = -(x,y,y) \cdot (a,b,c) = -(ax + by + cz)$, which is consistent with the plane equation $Ax + By + Cz + d = 0;$
offset $d = -(x,y,y) \cdot (a,b,c) = -(ax + by + cz)$, which is consistent with the plane equation $Ax + By + Cz + d = 0;$