## Thomas' Calculus 13th Edition

As we know that $\text{curl} F =(\dfrac{\partial R}{\partial y}-\dfrac{\partial Q}{\partial z})i +(\dfrac{\partial P}{\partial z}-\dfrac{\partial R}{\partial x}) k+(\dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y})k$ A vector field is conservative iff the $\text{curl} F =0$ Given: $F=y \sin z i+x \sin z j+xy \cos z k$ Now, $\text{curl} F =(x \cos z-x \cos z) i+(y \cos z-y \cos z)j +(\sin z-\sin z) k=0$ This shows that the vector field is Conservative.