A large, hollow sphere of internal radius R contains a smaller solid sphere of radius r. Write an inequality which would indicate that the small sphere has impacted the interior surface of the large sphere it occupies.
I think the best way to approach this is to assume that if the smaller sphere is contained within the larger sphere, no collision is detected.
I started by devising several inequality, all which must be true for the sphere to be within the other sphere:
x1 + r < x2 + r
y1 + r < y2 + r
z1 + r < z2 + r
How can I combine these into one inequality, assuming all above is correct?
Your inequalities only capture motion along one of the three coordinate axes. They must be true, but there are many cases where they are all true and the spheres touch. When the spheres touch, what is the distance between the centers?