Topics: Geometry - Line - 3D Space

Let and be two lines in .

We say and intersect on a point if they are different lines if there exists a point such that:


Given two lines in its general vectorial representation:

We can find their intersection by making them equal. This is the equation from where we start:

With that, we get the system with two variables and :

Solving this system gives us the intersection of the two lines. We can get three cases:

  1. There is one and only one solution the lines intersect (case 3)
  2. There are no solutions the lines never intersect
  3. There are infinite solutions the lines are actually the same line (i.e. they intersect everywhere; case 1)