product of vectors

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-18.12

https://metanorma.github.io/isq-smart/math/part-2-18/t2-18.12
urn:iso:std:iso:80000:-2:ed-2:en:item:2-18.12

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-18.12

IEC

urn:iec:std:iec:80000-2:2019:::item:2-18.12

Designations

ENproduct of vectors

FRproduit de vecteurs

Symbol

a \times b

Notation systems

AsciiMath

bb(ii(a)) xx bb(ii(b))

LaTeX

\mathbf{\mathit{a}} \times \mathbf{\mathit{b}}

Definition

vector product of $a$ and $b$

produit vectoriel de $a$ et $b$

Notes

The coordinates, in a right-handed Cartesian coordinate system, are

${(a \times b)}_{x} = a_{y} b_{z} - a_{z} b_{y}$

${(a \times b)}_{y} = a_{z} b_{x} - a_{x} b_{z}$

${(a \times b)}_{z} = a_{x} b_{y} - a_{y} b_{x}$

${(a \times b)}_{i} = \sum_{j} \sum_{k} ɛ_{i j k} a_{j} b_{k}$

See Levi-Civita symbol.

Les coordonnées, dans un système de coordonnées cartésiennes direct, sont:

${(a \times b)}_{x} = a_{y} b_{z} - a_{z} b_{y}$

${(a \times b)}_{y} = a_{z} b_{x} - a_{x} b_{z}$

${(a \times b)}_{z} = a_{x} b_{y} - a_{y} b_{x}$

${(a \times b)}_{i} = \sum_{j} \sum_{k} ɛ_{i j k} a_{j} b_{k}$

Voir Levi-Civita symbol.

Referenced by

multiplication

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:t2-18.12

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-18.12
skosxl:prefLabel	"product of vectors"@en
skosxl:altLabel	"bb(ii(a)) xx bb(ii(b))"@en
skos:definition	vector product of stem:[bb(ii(a))] and stem:[bb(ii(b))]
skos:note	The coordinates, in a right-handed Cartesian coordinate system, are stem:[(bb(ii(a)) xx bb(ii(b)))_x = a_y b_z - a_z b_…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-18

Related Entities

isq:MathConceptShape isq:part-2-18 smart:TermEntry