I can not seem to get this right

Find an equation of a sphere if one of its diameters has endpoints
(5, 5, 5) and (7, 7, 7).

1 answer

The center is at (6,6,6)
The diameter has length √12=2√3

so, the sphere is

(x-6)^2 + (y-6)^2 + (z-6)^2 = 3

It'd be better in the future if you provide some of your work when you get stuck.