Answer
a) $\dfrac{y}{z^2}i+\dfrac{z}{x^2}j+\dfrac{x}{y^2}k$
b) $\dfrac{1}{y}+\dfrac{1}{z}+\dfrac{1}{x}$
Work Step by Step
a) $curl F=(0+\dfrac{y}{z^2})i-(-\dfrac{z}{x^2}-0)j+(0+\dfrac{x}{y^2})k=\dfrac{y}{z^2}i+\dfrac{z}{x^2}j+\dfrac{x}{y^2}k$
b) $div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}$
$div F=\dfrac{\partial (\dfrac{x}{y})}{\partial x}+\dfrac{\partial \dfrac{y}{z}}{\partial y}+\dfrac{\partial (\dfrac{z}{x})}{\partial z}$
or, $=\dfrac{1}{y}+\dfrac{1}{z}+\dfrac{1}{x}$
