Linear algebra problem

[need_help]

Hi, I'm having trouble with this linear algebra problem. (Topic:algebraic vectors in R² and R³)

Here is the problem:

Let there be tangent spheres S₁ and S₂ where their respective volumes are V₁ and V₂.
(I Have added an Image given for the problem)

Determine the equations of S₁ and S₂ such that V_{1 =} 8*V_{2 .}

(Solution: -S₁: x² + y² + (z+2)² = 49
- S_2: ( x-3)² + (y+ 9/2 )² + (z+11)²= 49/4 )

I really don't know how to even start, so any advice or help would be of great help.
Thanks in advance!

 

[HallsofIvy]

You are told that one sphere has 8 times the volume of the other which, because volume is proportional to the cube of the radius, means the radius of one is twice the radius of the other. If "r" is the radius of the smaller sphere, then 2r is the radius of the other. Then the diameters are 2r and 4r so the total distance between the two points given is 6r. Find that distance from the coordinates given and set equal to 6r. That will give you the radii of the two spheres and you can find the centers of the two spheres from that.

 

[need_help]

Thanks a lot it worked!