Originally Posted by
Showcase_22 It seems like we're doing similar things! Do you have exams in May as well?
For this I would use the Component test for Conservative fields.
let $\displaystyle M(x,y,z)=yz$,$\displaystyle N(x,y,z)=xz$ and $\displaystyle P(x,y,z)=yz$.
For a field to be conservative $\displaystyle \frac{\partial P}{\partial y}=\frac{\partial N}{\partial z}$, $\displaystyle \frac{\partial M}{\partial z}=\frac{\partial P}{ \partial x}$ and $\displaystyle \frac{\partial N}{ \partial x}=\frac{\partial M}{\partial y}$.
But $\displaystyle \frac{\partial P}{\partial y}=z$ and $\displaystyle \frac{\partial N}{\partial z}=x$.
But we also know that $\displaystyle x=z$ since $\displaystyle yz=yz$.
Hence $\displaystyle \boxed{\frac{\partial P}{\partial y}=\frac{\partial N}{\partial z}}$
Try it for the others and see what you get. For me, it doesn't appear that $\displaystyle \frac{\partial M}{\partial z}=\frac{\partial P}{ \partial x}$ holds.....