Answer
a) $0$
b) $\dfrac{2}{\sqrt{x^2+y^2+z^2}}$
Work Step by Step
a) $curl F=curl(fG)=\nabla f \times G+f curl G$
Here, $\nabla f=-\dfrac{1}{(x^2+y^2+z^2)^{3/2}}(xi+yj+zk)$
$curl F=curl(fG)=\nabla f \times G+f curl G$
$=-\dfrac{1}{(x^2+y^2+z^2)^{3/2}}(xi+yj+zk) \times (xi+yj+zk)+0$
b) $div F=div(fG)=\nabla f \cdot G+f div G$
Here, $\nabla f=-\dfrac{1}{(x^2+y^2+z^2)^{3/2}}(xi+yj+zk) \cdot (xi+yj+zk)+\dfrac{1}{\sqrt{x^2+y^2+z^2}}\cdot (3)$
$div F=\dfrac{2}{\sqrt{x^2+y^2+z^2}}$
