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==Directed line segment==
{{further|Orientation (vector space)#On a line}}
{{see also|Relative position}}
When a line segment is given an [[orientation (vector space)|orientation]] (direction) it is called a '''directed line segment'''. It suggests a [[translation (geometry)|translation]] or [[displacement (geometry)|displacement]] (perhaps caused by a [[force]]). The magnitude and direction are indicative of a potential change. Extending a directed line segment semi-infinitely produces a ''[[ray (geometry)|ray]]'' and infinitely in both directions produces a ''directed line''. This suggestion has been absorbed into [[mathematical physics]] through the concept of a [[Euclidean vector]].<ref>Harry F. Davis & Arthur David Snider (1988) ''Introduction to Vector Analysis'', 5th edition, page 1, Wm. C. Brown Publishers {{isbn|0-697-06814-5}}</ref><ref>Matiur Rahman & Isaac Mulolani (2001) ''Applied Vector Analysis'', pages 9 & 10, [[CRC Press]] {{isbn|0-8493-1088-1}}</ref> The collection of all directed line segments is usually reduced by making "equivalent" any pair having the same length and orientation.<ref>Eutiquio C. Young (1978) ''Vector and Tensor Analysis'', pages 2 & 3, [[Marcel Dekker]] {{isbn|0-8247-6671-7}}</ref> This application of an [[equivalence relation]] dates from [[Giusto Bellavitis]]'s introduction of the concept of [[equipollence (geometry)|equipollence]] of directed line segments in 1835.
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