One of these is an impossible electrostatic field. Which one?
(a) E=k[xyx^+2yzy^+3xzz^];
(b) E=k[y2x^+(2xy+z2)y^+2yzz^].
Here k is a constant with the appropriate units. For the possible one, find the potential, using the origin as your reference point. Check your answer by computing ∇V. [Hint: You must select a specific path to integrate along. It doesn't matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a definite path in mind.]