Answer
(a) See the explanation below.
(b) See the explanation below.
(c) See the explanation below.
Work Step by Step
a) $F$ (vector field) can be defined on $\bf {R^3}$ as: $F=Ai+Bj+Ck$ where,$ i,j,k$ are the unit vectors.
$curl \space F=(C_y-B_z)i+(A_z-C_k)j+(B_x-A_y)k= \nabla \times F$
b) $F$ (vector field) can be defined on $\bf {R^3}$ as: $F=Ai+Bj+Ck$ where,$ i,j,k$ are the unit vectors.
$div \space F=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}=\nabla \cdot F$
c) $\bf{curlF}$ interprets the rotation of the fluid which aligns itself with the axis and $\bf{divF}$ interprets the diversion of the fluid, that is, the rate at which the fluid gets diverged or pushed away from the axis.
