position vector

Vector representing the position of a point with respect to a given origin and axes

Entitytype of vectorQ192388

Also known as location vector · radius vector · position

Instance of: type of vector
Subclass of: Euclidean vector
, physical quantity
, vector quantity

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O, and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P. In other words, it is the displacement or translation that maps the origin to P:

Overview

All data

45 statements · 13% with external sources · numbers in brackets are citations

Facet of: coordinate system
ISQ dimension: \mathsf{L}
Quantity symbol (LaTeX): \boldsymbol{r}
1
Sources
1.Stated in ISO 80000-3:2019 Quantities and units — Part 3: Space and time
View statement on Wikidata ↗
Recommended unit of measurement: metre
2
Sources
1.Stated in ISO 80000-3:2019 Quantities and units — Part 3: Space and time
2.Stated in ISO 80000-3:2006 Quantities and units — Part 3: Space and time
View statement on Wikidata ↗
Has characteristic: vector length
relative direction
reference point
Represents: physical location
Different from: bound vector
Defining formula: \begin{cases} \mathbf{a}=a\mathbf{i} \\ \mathbf{b}=b\mathbf{j} \\ \mathbf{c}=c\mathbf{k} \\ \end{cases} \therefore \begin{cases} \overline{OP}=\mathbf{a}+\mathbf{b}+\mathbf{c} \\ \mathbf{r}=a\mathbf{i}+b\mathbf{j}+c\mathbf{k} \\ \end{cases} \therefore \begin{cases} OL^2=a^2+b^2 \\ r=\sqrt{a^2+b^2+c^2} \end{cases}
In defining formula: \mathbf{a} symbol represents: component vector · applies to part: x-axis
\mathbf{b} symbol represents: component vector · applies to part: y-axis
\mathbf{c} symbol represents: component vector · applies to part: z-axis
a symbol represents: scalar quantity · applies to part: x-axis
b symbol represents: scalar quantity · applies to part: y-axis
c symbol represents: scalar quantity · applies to part: z-axis
\mathbf{i} symbol represents: unit vector along an axis · applies to part: x-axis
\mathbf{j} symbol represents: unit vector along an axis · applies to part: y-axis
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\mathbf{k} symbol represents: unit vector along an axis · applies to part: z-axis
\overline{OP} symbol represents: Euclidean vector
O symbol represents: coordinate origin
P symbol represents: point
\mathbf{r} symbol represents: radius
OL symbol represents: vector projection · applies to part: z-axis
L symbol represents: orthogonal projection · applies to part: z-axis

On other databases

15 identifiers linking position vector across the web's reference databases

Data quality

statements

13%

externally sourced

Source last edited September 10, 2026. AIDB refreshes this page daily.

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AIDB. (2026). position vector (Q192388). Retrieved from https://aidb.si/e/position-vector-Q192388