a) Determine the gradients of the functions A(q) = Ao sin(q · q) . where k R2 is a constant vector and B(q) = Bo sin(k . q) q (x, y) a position in R². = b) Determine the lines ye(x) where the functions take constant values. On a map these are contour lines. For a potential these are equipotential lines. c) Show that the gradient is oriented vertically to the contour lines. Hint: Consider a trajectory qe(t) = (x(t), ye(x(t))), and argue 1) that it describes the motion along a contour line, and 2) that (t) is therefore aligned parallel to the contour line.