Check that the point $(1,1,2)$ lies on the given surface. Then, viewing the surface as a level surface for a function $f(x,y,z)$, find a vector normal to the surface and an equation for the tangent plane to the surface at $(1,1,2)$. $$x^{2}-3y^{2}+z^{2} = 2$$

vector normal =

tangent plane:
$z =$