Hilbert space and hyperplanes

(10 points) Let V be a Hilbert space. Let S, and S, be two hyperplanes in V defined by S1 = (xEV |(al, x) = b1}, S2 = (x EV | (a2, x) = b2}. Let y E V be given. We consider the projection of y onto Sin S2, i.e., the solution of min llac - yl. (1) cesins2 (a) Prove that Sin S2 is convex. (b) Under which conditions on a1, a2, b1, b2, the set S, US, is convex