Line Segments that end at the same point

Question

Given the starting position and length of two line segments (P0, L0, P1, L2), find the configurations where both segments end at the same point. Both starting points can be anywhere in three dimensional space.

Answer 1

Imagine a sphere A with center $P_0$ and radius $L_0$ and a sphere B with center $P_1$ and radius $L_2$. The condition where the two line segments have the same end points is the same as the condition where the two spheres have at least one intersection. So, the condition will be

$|L_0-L_2| <= |\overrightarrow{P_0P_1}| <= L_0+L_2 $