Solution
= Solution
The <curl> is $\nabla\times\boldsymbol F_2=(2z,3z^2,0)$, which is not identically zero. A gradient of a smooth <scalar potential> has zero <curl>, so $\boldsymbol F_2$ is \b[not conservative] on $\mathbb R^3$.
= Solution
The <curl> is $\nabla\times\boldsymbol F_2=(2z,3z^2,0)$, which is not identically zero. A gradient of a smooth <scalar potential> has zero <curl>, so $\boldsymbol F_2$ is \b[not conservative] on $\mathbb R^3$.