# Soving intersection point for a sphere and sphere

How to find out the intersection point where a new sphere lands on other spheres with the same radius $$r$$. How can we find out the intersection point if we know the path of the incoming sphere as a straight line with known slope $$m$$, $$y$$-intercept $$c$$ and the coordinates of all other spheres on the plane? Using Line and circle intersection equation, I could solve the intersection point where a circular disc lands on another in two dimension. Now, I need to convert this two dimensional problem to three dimension by using spheres in place of circular discs as shown in Figure. Please suggest whether a simple line and sphere equation can solve my problem or I need to use any other method to solve the intersection point of a new incoming sphere with one of the many other spheres.

• Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. Oct 14, 2020 at 10:14
• Hi @srinivas This site expects you to show your work done so far asap. How deep are the spheres in the pool, what radius the impinging sphere has, how collisions are avoided etc. Oct 14, 2020 at 10:21
• Here, the depth of the pool is not necessary since the new incoming ball thrown towards the other balls will touch only on the surface. Here, the subsequent collisions can be ignored and it can be assumed that the new ball sticks to the spheres with which it makes its first contact. The radius of the sphere is a variable $r$ and all the spheres have the same radius. Oct 14, 2020 at 11:09