Chapter 13.2, Problem 13.80P

The force F = (yzi + zxj + xyk)/xyz acts on the particle P(x, y, z) which moves in space. (a) Using the relation derived in Prob. 13.79, show that this force is a conservative force. (b) Determine the potential function associated with F.

*13.79 Prove that a force F(x, y, z) is conservative if, and only if, the following relations are satisfied:

$\frac{\partial F_x}{\partial y}=\frac{\partial F_y}{\partial x}\frac{\partial F_y}{\partial z}=\frac{\partial F_z}{\partial y}\frac{\partial F_z}{\partial x}=\frac{\partial F_x}{\partial z}$