Please answer both because they are related

(1) (4+4 points) Consider the vector field F : R3 - R', F(x, y, z) = (sin(y) + z cos(x), x cos(y) + sin(z), y cos(z) + sin(x)). (a) Compute curl( F) (x, y, z). (b) Is F a gradient field? If so, find a potential f of F. (2) (2+2 points) Let F be as in problem (1). (a) Compute div(F)(z, y, z ). (b) Is the origin a sink, source or balanced point of F