Given $Fin{C}^1(R^3)$ with non$-$vanishing first order partial derivatives satisfying $F(x,y,z)=0,$ prove that $\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{y}}\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}\text{z}}\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}=-1$ on $R^3.$