Vectors - Sphere Problem

Question

Find the equation of the sphere if one of its diameters has endpoints (0,10,3) and (2,14,9).

I got (x - 1)^2 + (y - 12)^2 + (z - 6)^2 - (sqrt(56) / 2) = 0

But this is not correct.

If you could explain step-by-step, that would be very helpful.

Answer 1

if the diameter endpoints are (0,10,3) and (2,14,9)

the diameter = sqr(4+16+36) =sqr56 =2sqr14

sphere's equation is (x-h)^2 + (y-k)^2 + (z-l)^2 = r^2 = (2sqr14/2)^2 = 14, where (h,k,l) is the center of the sphere and r=radius

center is the midpoint between the endpoints = (1,12,6)

(x-1)^2 + (y-12)^2 +(z-6)^2 = 14

you had it all right, except for squaring the radius