Cartesian coordinate

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-17.1

https://metanorma.github.io/isq-smart/math/part-2-17/t2-17.1
urn:iso:std:iso:80000:-2:ed-2:en:item:2-17.1

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-17.1

IEC

urn:iec:std:iec:80000-2:2019:::item:2-17.1

Designations

ENCartesian coordinate

FRcoordonnée cartésienne

Symbol

x, y, z

Notation systems

AsciiMath

x, y, z

LaTeX

x , y , z

Definition

$r = x e_{x} + y e_{y} + z e_{z}$ +

$d r = d x e_{x} + d y e_{y} + d z e_{z}$

$r = x e_{x} + y e_{y} + z e_{z}$ +

$d r = d x e_{x} + d y e_{y} + d z e_{z}$

Notes

The base vectors $e_{x}, e_{y}, e_{z}$ form an orthonormal system (i.e. the vectors are unit vectors and orthogonal) which is right-handed, see fig1;and!fig4.

$e_{1}, e_{2}, e_{3}$ or $i, j, k$ are also used for the base vectors and $x_{1}, x_{2}, x_{3}$ or $i, j, k$ for the coordinates.

Les vecteurs de base $e_{x}, e_{y}, e_{z}$ forment un trièdre orthonormé direct (c'est-à-dire que les vecteurs sont des vecteurs unités et orthogonaux), voir fig1;and!fig4.

On utilise aussi $e_{1}, e_{2}, e_{3}$ ou $i, j, k$ pour les vecteurs de base et $x_{1}, x_{2}, x_{3}$ ou $i, j, k$ pour les coordonnées.

Ontology
isq:MathConcept smart:TermEntry

Class Hierarchy

smart:Entity smart:TermEntryisq:MathConcept

A mathematical concept as defined in ISO/IEC 80000 Part 2.

Instance IRI

isq:t2-17.1

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-17.1
skosxl:prefLabel	"Cartesian coordinate"@en
skosxl:altLabel	"x, y, z"@en
skos:definition	stem:[bb(ii(r)) = xbb(ii(e))_x + ybb(ii(e))_y + zbb(ii(e))_z] + stem:["d"bb(ii(r)) = "d"x" "bb(ii(e))_x + "d"y" "bb(ii(e…
skos:note	The base vectors stem:[bb(ii(e))_x, bb(ii(e))_y, bb(ii(e))_z] form an orthonormal system (i.e. the vectors are unit vect…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-17

Related Entities

isq:MathConceptShape isq:part-2-17 smart:TermEntry