Which point on the sphere S:$x^2+y^2+z^2=1$ is farthest from the Point P $(2,1,3)$?

Question

I have tried to use Lagrange Mulitplier here to maximize $$F:(x-2)^2+(y-1)^2+(z-3)^2$$ subject to the constraint of S, i.e $$\nabla{F}=\lambda.\nabla{S}$$and got $\lambda=1\pm\sqrt{14}$, which in turn gives values for $(x,y,z)$ as $\frac{1}{\sqrt{14}}(\pm2,\pm1,\pm3)$. I dont know how to narrow down my choice to find my point. Kindly help.