# Beam (geometry)

In geometry , a **ray** or a **half-line** is - to put it clearly - a straight line that is limited on one side, but extends to infinity on the other side.

- A
*half line*is a geometric object that is created when a point divides a straight line on which it lies. The point is either part of the half-line or not. - A
*ray*has an orientation : It starts from a starting point .

*Rays* and *half-straight lines* must therefore be distinguished from *straight lines* that are unlimited on both sides and lines that are limited on both sides.

## Geometric representation

The notation used in the sketch expresses that it is a subset of the straight line that is bounded by the point , but extends beyond the point .

With the help of the intermediate relation ("... lies between ... and ...") the half-line can be defined as the set of all points on the line for which is not between and .

Considering a straight line and an arbitrary point on , as the two blank half-lines defined thereby , and characterized as a non-empty subsets of which fulfill the following conditions:

- Every point on the straight line that does not coincide with belongs to exactly one of the two subsets or .
- If any point is from and any point from , then lies between and .

This means that the half-line is closely related to the term *interval* : An interval can be defined as the intersection of two half-lines.

## Analytical representation

In analytic geometry , the half-line corresponds to the set of all points whose position vector is given by

- with .

Where and are the position vectors of the endpoints and . is the ( real ) parameter of this parametric equation .