I am having real difficulty knowing how to approach this question, so any help or pointers would be appreciated.
Consider the vector field:
$$ \vec{G} = -3xz^2\vec{i} + z^3\vec{k} $$
FInd a vector field $\vec{F}$, such that:
$$ \vec{G} = \nabla \times \vec{F} $$
Hint: Look for a vector field in the form $ \vec{F} = F\vec{j}$
I am assuming I am looking for a way to exploit the fact that the $\vec{j}$ term in the original vector field is zero?
Many thanks to anyone who can help.
Definition of the curl is $$ -3xz^2\mathbf{i} + z^3\mathbf{k} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k}\\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z}\\ F_x & F_y & F_z \end{vmatrix} $$ Then you evaluate the determinant.