1. ## consevative field hep

Okay, have you not tried this yourself? The standard calculation for $\nabla\times G$ is $\left|\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ 2xyz & x^2z+2y & x^2y- 2z \end{array}\right|$. You knew that didn't you? The result is is very simple as you should suspect because the next part is "show that G is a conservative field". What must be true of $\nabla\times G$ in order that the field be conservative? And what is true about the work done in moving an object around a closed path in a conservative force field?