Let $\displaystyle f : U \to \mathbb{R}^3 $ be a surface element. Suppose that the image of $\displaystyle f $ lies in the region $\displaystyle \{(x, y, z) | z > 0 \} $, and the principal curvatures of $\displaystyle f $ at $\displaystyle f(0) $ satisfy $\displaystyle \kappa_1 \kappa_2 < 0 $. Show the tangent plane of $\displaystyle f $ at that point is not parallel to the $\displaystyle xy $ axis.