Let F: R R be a C function and S = {(x, y, z) E R: F(r, y, z) = 0} be a level set. (a) Let a(t) (x(t), y(t), z(t)) be a differentiable curve with a(t) e S for all t e R. Show that if VF(a(0)) and a'(0) are both non-zero, then they are perpendicular to each other. (b) Let (a, b, c) E S and VF(a, b, c) # 0. Let (p, q,r) 0 be perpendicular to VF(a, b, c). Show that there exists & > 0 and a differentiable curve B(t) such that B(t) ES for -6