A scalar potential [tex]\(\phi\)[/tex] and a vector field [tex]\(\vec{F}\)[/tex] are given by [tex]\(\phi = 2x^3yz + 3xy\)[/tex] and [tex]\(\vec{F} = 2x^2yz \hat{i} + 4xyz^3 \hat{j} + 3xy^2z \hat{k}\)[/tex]. Determine at the point [tex]\((1,2,1)\)[/tex]:

(i) [tex]\(\nabla \phi\)[/tex];

(ii) [tex]\(\nabla \cdot \vec{F}\)[/tex];

(iii) [tex]\(\nabla \times \vec{F}\)[/tex].