Find the minimal distance between any point on the sphere

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How can we find the minimal distance between any point on the sphere whose centre is 2,1,3 and radius is 1 and any point on the sphere centred at -3,2,4 and radius is 4?


is there any formula for finding this minimum distance ?
 
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find the distance between the centres, and subtract the sum of radii of the spheres...
 


thnx aniketp...that was helpful...i got my answer
 


no problem, but i hope you understood WHY this works.
 


well...yes...i have a math exam tomorrow...have to finish a LOT of things
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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