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## Homework Statement

Find the set of points [tex](a,b,c)[/tex] for which the spheres below intersect orthogonally.

sphere 1: [tex]f(x,y,x):x^2+y^2+z^2=1[/tex]

sphere 2: [tex]g(x,y,z):(x-a)^2+(y-b)^2+(z-c)^2=1[/tex]

## The Attempt at a Solution

II know that the gradient vector, [tex]\nabla f[/tex], is normal to the surface determined by [tex]f[/tex], I'm just unclear on creating the connection to the either the gradient or surface of [tex]g[/tex]. Clarification would be great.

Thanks