Solving the Equation of a Sphere with Diameter Endpoints

[mamma_mia66]

Homework Statement

Write the equation of the sphere whose diameter has endpoints at (-1,1,-3) and (3,-1,2).

Homework Equations

The Attempt at a Solution

(x-x₁)²+ (y-y₁)²+ (z-z₁)²= r²

the center of the sphere is : (1,0,-1/2)
r= $$\sqrt{}5/4$$

then the equation is: (x-1)²+(y-0)²+(z+1/2)²=5/4

Please someone check my answer and if I am not right, help me to solve it.

 

[tiny-tim]

the center of the sphere is : (1,0,-1/2)
r= $$\sqrt{}5/4$$

Hi mamma_mia66!

Centre is right.

But r is wrong. ​

(you've calculated the distance from the centre to the origin! )

 

[mamma_mia66]

I am not sure that I know how to find the r ? too old to remember it after so many years not being in school.

 

[tiny-tim]

Yes you do!

they've given you a diameter … ​

 

[mamma_mia66]

r= sq. rt. (3-1)²+ (1-0)²+(2-1/2)²= 21/4