If \(\vec{A}=\vec{\nabla}\phi\) and \(\phi = xy+yz+zx\), then the true statements are:
A. \(\vec{\nabla}\cdot\vec{A}=0\)
B. \(\vec{\nabla}\cdot\vec{A}\neq0\)
C. \(\vec{\nabla}\times\vec{A}=\vec{0}\)
D. \(\vec{\nabla}\times\vec{A}\neq\vec{0}\)
Choose the correct answer from the option given below: