Let $\displaystyle f(x,y,z) = x^2 + 2y^2 + 3z^2$ and let S be the isotimic surface: $\displaystyle f = 1$. Find all the points $\displaystyle (x,y,z)$ on S that have tangent planes with normals $\displaystyle (1,1,1)$.

I'm not even sure where to begin...