We consider the vector field: (i) (ii) : R R, (x, y, z) = sin z +6y2 -2x -3 cos x : Show that this vector field has a vector potential. : Determine a vector potential a of the form (x, y, z) = (0, a2(x, y, z)), a3(x, y, z)), (x, y, z) = R R3 with continuously partially differentiable functions a2, a3: R R