Is it possible for G of x comma y comma z equal to angle bracket sine x comma cosine y comma sine parentheses x times yz close parentheses close angle bracket to be the curl of a vector field? In order to determine this we want to find the divergence of G, which we know is p sub x plus q sub y plus r sub z. So the divergence of G is equal to cosine x minus sine y plus xy times cosine parentheses xyz close parentheses.

And this is not equal to 0. So the answer is no. So for a more detailed explanation, OK, the divergence of G is equal to, well, this quantity we just found. If G were the curl vector field F, then the divergence of G would be the divergence of the curl of F, and that would be equal to 0. But the divergence of G is not 0, and therefore G is not the curl of any other vector field.