Line–line intersection

In analytic geometry, the intersection of a line and a line can be the empty set, a point, or a line. Distinguishing these cases, and determining equations for the point and line in the latter cases have use, for example, in computer graphics, motion planning, and collision detection.

3D Euclidean space

The study of linear intersections in Euclidean space is often used as a motivation for the solution of systems of linear equations and can form a basis for the study of linear algebra. The entry titled System of linear equations provides an analytic treatment of this topic.

Non-Euclidean space

The number and location of possible intersections between two lines and the number of possible lines with no intersections (parallel) with a given line are the distinguishing features of Non-Euclidean geometry. The entry titled Parallel postulate provides additional background on this topic.