Intersection between a line and a sphere

Question

I\'m trying to find the point of intersection between a sphere and a line but honestly, I don\'t have any idea of how to do so. Could anyone help me on this one ?

Answer 1

You may use Wolfram Alpha to solve it in the coordinate system where the sphere is centered.

In this system, the equations are:

Sphere:

     x^2 + y^2 + z^2 = r^2  

Straight line:

    x = x0 + Cos[x1] t
    y = y0 + Cos[y1] t
    z = z0 + Cos[z1] t 

Then we ask Wolfram Alpha to solve for t: (Try it!)

and after that you may change again to your original coordinate system (a simple translation)