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) When $F=ai+bj+ck$, then we have $curl F=[c_y-b_z]i+[a_z-c_z]j+[b_x-a_y]k$
$curl F=(0-e^y \cos z)i+(0-e^z \cos x)j+(0-e^x \cos y)k=-e^y \cos zi-e^z \cos xj-e^x \cos yk$
b) $div F=\dfrac{\partial [e^x \sin y]}{\partial x}+\dfrac{\partial [e^y \sin z]}{\partial y}+\dfrac{\partial [e^z \sin x]}{\partial z}=e^x \sin y+e^y \sin z+e^z \sin x$
