For the given vector field, find the divergence and curl of the field.

a. \(\mathbf{F}=x \mathbf{i}+y \mathbf{j}\)

b. \(\mathbf{F}=\frac{y}{r} \mathbf{i}-\frac{x}{r} \mathbf{j}\), for \(r=\sqrt{x^{2}+y^{2}}\).

c. \(\mathbf{F}=x^{2} y \mathbf{i}+z \mathbf{j}+x y z \mathbf{k}\).