Answer
a) $-e^y \cos zi-e^z \cos xj-e^x \cos yk$
b) $e^x \sin y+e^y \sin z+e^z \sin x$
Work Step by Step
a) $curl F=(0-e^y \cos z)i+(0-e^z \cos x)j+(0-e^x \cos y)k$
or, $=-e^y \cos zi-e^z \cos xj-e^x \cos yk$
b) $div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}$
$div F=\dfrac{\partial (e^x \sin y)}{\partial x}+\dfrac{\partial (e^y \sin z)}{\partial y}+\dfrac{\partial (e^z \sin x)}{\partial z}$
or, $=e^x \sin y+e^y \sin z+e^z \sin x$
