# A force field is described by <F_x,F_y,F_z> = < x , z, 2y -z > . Is this force field conservative?

Aug 30, 2016

field is not conservative

#### Explanation:

$\vec{\nabla} \times \vec{F} =$

$\det \left(\begin{matrix}\hat{i} & \hat{j} & \hat{k} \\ {\partial}_{x} & {\partial}_{y} & {\partial}_{z} \\ x & z & 2 y - z\end{matrix}\right)$

$= \hat{i} \left(2 - 1\right) - \hat{j} \left(0\right) + \hat{k} \left(0\right) = \left(\begin{matrix}1 \\ 0 \\ 0\end{matrix}\right) \ne \vec{0}$

So the field is not conservative