Question on Equidistance: points equid. from three others

[emgraham]

I am trying to find the equation of a line with points that are equidistance from three points in 3D space. I think this will be a sphere but I do not know how to find the equation. The three points are (2,1,3), (3,-4,-1) and (2,1 -1). Any help on this would be greatly appreciated.
Thanks, Erika

 

[pka]

Write the line that is the perpendicular bisector of (2,1,3) and (3,-4,-1).
Write the line that is the perpendicular bisector of (2,1,3) and (2,1 -1).
Then find the point of intersection of the two lines.
That is your center.