Answer
$0$
Work Step by Step
$Jacobian =\begin{vmatrix} \dfrac{\partial x}{\partial u}&\dfrac{\partial x}{\partial v}&\dfrac{\partial x}{\partial w}\\\dfrac{\partial y}{\partial u}&\dfrac{\partial y}{\partial v}&\dfrac{\partial y}{\partial w}\\\dfrac{\partial z}{\partial u}&\dfrac{\partial z}{\partial v}&\dfrac{\partial z}{\partial w}\end{vmatrix}$
Now, $Jacobian=\begin{vmatrix} 1/v&-u/v^2&0\\0&1/w&-v/w^2\\-w/u^2&0&1/u\end{vmatrix}=(\dfrac{1}{v})(\dfrac{1}{w}\dfrac{1}{u})-(\dfrac{-v}{w^2}(0))+\dfrac{u}{v^2}[0-(\dfrac{-w}{u^2}\dfrac{-v}{w^2}]=\dfrac{1}{uvw}-\dfrac{1}{uvw}=0$
