# Thread: Curl of Vector Field

1. ## Curl of Vector Field

Find the curl of vector field.

F(x, y, z) = xyz i - x^2 y k

∇xF = 0

No curl in this vector field.

The book's answer is

∇xF = -x^2 i + 3xy j - xz k

Who is right and why?

2. ## Re: Curl of Vector Field

Originally Posted by USNAVY
Find the curl of vector field.
F(x, y, z) = xyz i - x^2 y k
∇xF = 0
No curl in this vector field.
The book's answer is
∇xF = -x^2 i + 3xy j - xz k
Who is right and why?
$\nabla\times F=\left| {\begin{array}{*{20}{c}} {\partial x}&{\partial y}&{\partial z} \\ {xyz}&0&{ - {x^2}y} \end{array}} \right| = - {x^2}i + 3xyj - xzk$

It appears that the textbook is correct.

3. ## Re: Curl of Vector Field

It is very easy to make simple sign errors when calculating the determinant for the curl F. I believe this to be my problem.