Multivariable calculus

29. Determine whether each statement is true or false. Justify / explain. (a) There is a non-constant vector field F(x, y, z) such that curl (v ) =div ( F ). (b) If F(x, y, z) = (sin(z), cos(z), 0), then curl (curl curl ( F) F (c) If the divergence of F is zero, then F is a gradient vector field. (d) If F and G are two vector fields for which the divergence is the same, then F - G is a constant vector field