(Multivariable Calc) Given four points, find a sphere.help me.

[Vampire]

Homework Statement

Find the radius and center for the sphere determined by the four points
(3,2,-1), (5,-2,1), (-3,1,2), (0,2,4).
Give the exact location of the center but approximate the radius to the nearest 0.1.

Homework Equations

Equation of a sphere: x² + y² + z² + Gx +Hy +Iz +J = 0
or C(h,k,l) (x-h)² + (y-k)² + (z-l)² - r² = 0

There's also a 5x5 matrix with the determinant equal to zero, but I have no idea how to use it (seen at line 29 here: http://mathworld.wolfram.com/Sphere.html). I believe this is beyond 12.1 in multivariable calculus.

The Attempt at a Solution

I tried to use the determinant formula, but I got lost as I don't even know how to use it.

Is there any other way?

EDIT: Solved. Thank you.

 

[rock.freak667]

(x-h)² + (y-k)² + (z-l)² - r² = 0

Using this, I'd just substitute the 4 coordinates to get me 4 equations with 4 unknowns in them. Then just use row reduction to get h,k,l and r

 

[Vampire]

So I can substitute, then treat the different lines as a system of equations?

 

[rock.freak667]

So I can substitute, then treat the different lines as a system of equations?

well your variables would be h²,k²,l²,r² and not h,k,l,r like I previously said.

 

[Vampire]

Alright I will try that. Thank you very much.