A surface is given by \(z^{2}=2x^{2}-y^{2}\) and \(\vec{n}\) and \(-\vec{n}\) are unit normal vectors to the surface at the point \(\vec{P}=\hat{\imath}+\sqrt{2}\,\hat{k}\). Which of the following vectors can be \(\vec{n}\), where \(\hat{\imath}\), \(\hat{\jmath}\) and \(\hat{k}\) are the unit vectors along \(x\), \(y\) and \(z\) axes, respectively?