# Thread: Find Curl of Vector Field

1. ## Find Curl of Vector Field

Find the curl of vector field.

F(x, y, z) = xy i + yz j + xy k

∇xF = x^2 • z i + y^2•x j + z^2 k

∇xF = -y i - z j - x k

Who is right and why?

2. ## Re: Find Curl of Vector Field

Originally Posted by USNAVY
Find the curl of vector field.

F(x, y, z) = xy i + yz j + xy k

∇xF = x^2 • z i + y^2•x j + z^2 k

∇xF = -y i - z j - x k

Who is right and why?

Show some effort on your part.

3. ## Re: Find Curl of Vector Field

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.

4. ## Re: Find Curl of Vector Field

Originally Posted by USNAVY
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.

5. ## Re: Find Curl of Vector Field

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.

$\nabla\times F= \left|\begin{array}{ccc} \vec{i} & \vec{j} & \vec{k} \\ \frac{\partial F}{\partial x} & \frac{\partial F}{\partial y} & \frac{\partial F}{\partial z} \\ xy & yz & xz \end{array}\right|= (0- x)\vec{i}-(z- 0)\vec{j}+ (0- x)\vec{k}= -x\vec{i}- \vec{j}- \vec{k}$.