D. Let P be a projection on an inner product space V. Prove that the following are equivalent: (a) P is an orthogonal projection. (b) 1/v/12 = 1/Pv/12 + |/v - Pv//2 for all v E V. (c) || Pull 0. Compute | |v - tw||2 - ||v||2 for small t > 0. For (d) (a), show that (Pv, (1 - P) w) = 0