(a) Let F1 = x2 z and F2 = x x + y y + z z. Calculate the divergence and curl of F1 and F2. Which one can be written as the gradient of a scalar? Find a scalar potential that does the job. Which one can be written as the curl of a vector? Find a suitable vector potential.

(b) Show that F3 = yzx + zxy + xyz can be written both as the gradient of a scalar and as the curl of a vector. Find scalar and vector potentials for this function.