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Glyph for U+2A2F
Source: Noto Sans Math

U+2A2F Vector Or Cross Product

U+2A2F was added to Unicode in version 3.2 (2002). It belongs to the block U+2A00 to U+2AFF Supplemental Mathematical Operators in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script.

The glyph is not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is not mirrored. The glyph can, under circumstances, be confused with 1 other glyphs. In text U+2A2F behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

The CLDR project labels this character “vector cross product” for use in screen reading software.

The Wikipedia has the following information about this codepoint:

In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E {displaystyle E} ), and is denoted by the symbol × {displaystyle imes } . Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, and thus normal to the plane containing them. The units of the cross-product are the product of the units of each vector. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product).

If two vectors have the same direction or have the exact opposite direction from each other (that is, they are not linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths.

The cross product is anticommutative (that is, a × b = − b × a) and is distributive over addition (that is, a × (b + c) = a × b + a × c). The space E {displaystyle E} together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.

Like the dot product, it depends on the metric of Euclidean space, but unlike the dot product, it also depends on a choice of orientation (or "handedness") of the space (it's why an oriented space is needed). In connection with the cross product, the exterior product of vectors can be used in arbitrary dimensions (with a bivector or 2-form result) and is independent of the orientation of the space.

The product can be generalized in various ways, using the orientation and metric structure just as for the traditional 3-dimensional cross product, one can, in n dimensions, take the product of n − 1 vectors to produce a vector perpendicular to all of them. But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions. The cross-product in seven dimensions has undesirable properties, however (e.g. it fails to satisfy the Jacobi identity), so it is not used in mathematical physics to represent quantities such as multi-dimensional space-time. (See § Generalizations, below, for other dimensions.)

Representations

System Representation
10799
UTF-8 E2 A8 AF
UTF-16 2A 2F
UTF-32 00 00 2A 2F
URL-Quoted %E2%A8%AF
HTML hex reference ⨯
Wrong windows-1252 Mojibake ⨯
HTML named entity ⨯
LATEX \ElzTimes

Related Characters

Confusables

Elsewhere

Complete Record

Property Value
Age 3.2 (2002)
Unicode Name VECTOR OR CROSS PRODUCT
Unicode 1 Name
Block Supplemental Arrows-C
General Category Math Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Glyph for U+2A2F Vector Or Cross Product
Lowercase
Simple Lowercase Mapping Glyph for U+2A2F Vector Or Cross Product
Lowercase Mapping Glyph for U+2A2F Vector Or Cross Product
Uppercase
Simple Uppercase Mapping Glyph for U+2A2F Vector Or Cross Product
Uppercase Mapping Glyph for U+2A2F Vector Or Cross Product
Simple Titlecase Mapping Glyph for U+2A2F Vector Or Cross Product
Titlecase Mapping Glyph for U+2A2F Vector Or Cross Product
Case Folding Glyph for U+2A2F Vector Or Cross Product
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Composition Exclusion
Case Ignorable
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Cased
Full Composition Exclusion
Default Ignorable Code Point
Dash
Deprecated
Diacritic
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji Presentation
Emoji
Extender
Extended Pictographic
FC NFKC Closure Glyph for U+2A2F Vector Or Cross Product
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Grapheme Link
Hex Digit
Hyphen
ID Continue
ID Start
IDS Binary Operator
IDS Trinary Operator and
IDSU 0
ID_Compat_Math_Continue 0
ID_Compat_Math_Start 0
Ideographic
InCB None
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
Jamo Short Name
Join Control
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Glyph for U+2A2F Vector Or Cross Product
NFKC Quick Check Yes
NFKC_SCF Glyph for U+2A2F Vector Or Cross Product
NFKD Quick Check Yes
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Prepended Concatenation Mark
Pattern Syntax
Pattern White Space
Quotation Mark
Regional Indicator
Radical
Sentence Break Other
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Variation Selector
Word Break Other
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD
Bidi Paired Bracket Glyph for U+2A2F Vector Or Cross Product
Bidi Paired Bracket Type None
East Asian Width Neutral
Hangul Syllable Type Not Applicable
ISO 10646 Comment
Joining Group No_Joining_Group
Joining Type Non Joining
Line Break Alphabetic
Numeric Type None
Numeric Value not a number
Simple Case Folding Glyph for U+2A2F Vector Or Cross Product
Script Extension
Vertical Orientation R