Note that the distance, d, between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a 3-dimensional rectangular system is
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y{1})^{2}+(z_{2}-z_{1})^{2}} [/tex]
Therefore, the length of the diameter of the sphere is
[tex]d = \sqrt{(6-2)^{2}+(5-3)^{2}+(7-5)^{2}} = \sqrt{24} [/tex]
The radius is
r = d/2 = √(24)/2=√6
or
r² = 6
The center of the sphere is
[tex]( \frac{2+6}{2}, \frac{3+5}{2}, \frac{5+7}{2}) = (4, 4, 6). [/tex]
Answer:
The equation of the sphere is
(x-4)² + (y-4)² + (z-6)² = 6
