*dot P,Q = Moving anywhere in Sphere

*dot P1Q1 = dot PQ (orthogonal projection) Sphere to Square(y+/3z+8-0)

*dotP2Q2 = dot PQ (orthogonal projection)
Sphere to Square(y=4)


You should get answer:

2lPQl^2 - lP1Q1l^2 - lP2Q2l^2

Maximum?

*l-2l , l2l = 2