Find minimum distance between any point on the sphere $\displaystyle (x-2)^2+(y-1)^2+(z-3)^2=1 $and any point on the sphere $\displaystyle (x+3)^2+(y-2)^2+(z-4)^2=4$.

I find the distance between the two center,in which is [tex]3\sqrt{3}[\MATH]. Then I substract the distance between 2 center by both the radii of the sphere, that is, I get the minimum distance to be [tex]3\sqrt{3}-1-2=3\sqrt{3}-3[\MATH].