Let V be a Hilbert space. Let S1 and S2 be two hyperplanes in V defined by Let S₁ = {x EV | (a1, x) = b₁}, S₂ = {x = V | (a2, x) = b2}. y Є V be given. We consider the projection of y onto S₁n S2, i.e., the solution of min ||xy|. xES₁NS2 (1) (a) Prove that S₁ S₂ is a plane, i.e., if x, z Є S₁ П S2, then (1+t)z – tx € S₁ П S₂ for any t € R. (b) Prove that z is a solution of (1) if and only if z Є S₁ П S2 and (zy, zx) = 0, Va Є S₁n S2. (c) Find an explicit solution of (1). (d) Prove the solution found in part (c) is unique.