Let P denote orthogonal projection of R3 onto the plane V = {z = x + y)

Question:

Let P denote orthogonal projection of R3 onto the plane V = {z = x + y) and Q denote orthogonal projection onto the plane W = {z = x - y). Is the composition R = Q ○ P the same as orthogonal projection onto the line L = V ⋂ W? Verily your conclusion by computing the matrix representatives of P, Q, and R.