I actually have a suspicion that there is a typo in the question. I think the last term of the vector field should be xz k instead of xy k. When it is xz k, then my answer agrees with the textbook.
I actually have a suspicion that there is a typo in the question. I think the last term of the vector field should be xz k instead of xy k. When it is xz k, then my answer agrees with the textbook.
Well find $\nabla F$ and show it. Then explain how it differs from the text.
The book's answer is correct. I can't imagine how you got your answer! Your answer has polynomials of higher power than the original vector while differentiating always reduces the power of a polynomial.