Line-line intersection

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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.

[edit] 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.

[edit] 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.