# Definition:Directed Line Segment

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## Definition

A **directed line segment** is a line segment endowed with the additional property of direction.

It is often used in the context of applied mathematics to represent a vector quantity.

This article is complete as far as it goes, but it could do with expansion.In particular: Perhaps the above statement should also be expanded to allow a D.L.S. to be defined as a vector quantity applied at a particular point. There is a danger (as pointed out on the Definition:Vector Quantity page) of implying / believing that a vector, in general, is applied at a particular point, for example usually the origin. Thus, this page allows the opportunity to consider a definition of an object which consists of a vector "rooted" at a particular point, as a convenient fiction for what is actually happening in the context of physics.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

This article is incomplete.In particular: needs a picture
It may be worthwhile to point out that this can be formalized with an ordered pair. Establish connection with Definition:Affine SpaceYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by expanding it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Stub}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Also known as

A **directed line segment** can also be seen as **oriented line segment**.

## Sources

- 1936: Richard Courant:
*Differential and Integral Calculus: Volume $\text { II }$*... (previous) ... (next): Chapter $\text I$: Preliminary Remarks on Analytical Geometry and Vector Analysis: $1$. Rectangular Co-ordinates and Vectors: $2$. Directions and Vectors. Formulæ for Transforming Axes - 1947: William H. McCrea:
*Analytical Geometry of Three Dimensions*(2nd ed.) ... (previous) ... (next): Chapter $\text I$: Coordinate System: Directions: $\S 1$. Introductory: Nomenclature - 1961: I.M. Gel'fand:
*Lectures on Linear Algebra*(2nd ed.) ... (next): $\S 1$: $n$-Dimensional vector spaces - 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text V$: Vector Spaces: $\S 26$. Vector Spaces and Modules - 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 22$: Vectors and Scalars - 1972: M.A. Akivis and V.V. Goldberg:
*An Introduction to Linear Algebra & Tensors*(translated by Richard A. Silverman) ... (previous) ... (next): Chapter $1$: Linear Spaces: $1$. Basic Concepts - 1992: Frederick W. Byron, Jr. and Robert W. Fuller:
*Mathematics of Classical and Quantum Physics*... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.1$ Geometric and Algebraic Definitions of a Vector