[SOLVED] Minimize distance

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
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
Aug 2006
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8,631
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
Mar 2010
3,093
582
Florida
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 \(\displaystyle 3\sqrt{3}-2\)