# [SOLVED] Minimize distance

#### dwsmith

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

I forgot how to do these type of problems.

#### Plato

MHF Helper
Find the minimal distance between any point on the sphere $$\displaystyle (x-2)^2+(y-1)^2+(z-3)^2=1$$ and $$\displaystyle (x+3)^2+(y-2)^2+(z-4)^2=4$$.
What is the distance between the centers of the spheres?

#### dwsmith

MHF Hall of Honor
What is the distance between the centers of the spheres?
$$\displaystyle 3\sqrt{3}$$

#### Plato

MHF Helper
$$\displaystyle 3\sqrt{3}$$
The radius of one sphere is 1 and the radius of the other is 2.
SO?

#### dwsmith

MHF Hall of Honor
The radius of one sphere is 1 and the radius of the other is 2.
SO?
The spheres don't overlap so the min distance is $$\displaystyle 3\sqrt{3}-2$$

#### Plato

MHF Helper
The spheres don't overlap so the min distance is $$\displaystyle 3\sqrt{3}-\color{red}3$$
!

• dwsmith