Home U+2A00 to U+2AFF Supplemental Mathematical Operators

# 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. It assigns additional tags, e.g. for search in emoji pickers: vector cross product.

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. 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 (e.g. it fails to satisfy the Jacobi identity), however, 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-Escape &#x2A2F;
Wrong windows-1252 Mojibake â¨¯
HTML-Escape &Cross;
LATEX \ElzTimes

## 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 Vector Or Cross Product
Lowercase
Simple Lowercase Mapping Vector Or Cross Product
Lowercase Mapping Vector Or Cross Product
Uppercase
Simple Uppercase Mapping Vector Or Cross Product
Uppercase Mapping Vector Or Cross Product
Simple Titlecase Mapping Vector Or Cross Product
Titlecase Mapping Vector Or Cross Product
Case Folding Vector Or Cross Product
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Bidi Paired Bracket Vector Or Cross Product
Bidi Paired Bracket Type None
Cased
Composition Exclusion
Case Ignorable
Full Composition Exclusion
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Dash
Deprecated
Default Ignorable Code Point
Diacritic
East Asian Width Neutral
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji
Emoji Presentation
Extender
Extended Pictographic
FC NFKC Closure Vector Or Cross Product
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Hex Digit
Hangul Syllable Type Not Applicable
Hyphen
ID Continue
Ideographic
ID Start
IDS Binary Operator
IDS Trinary Operator and
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
ISO 10646 Comment
Joining Group No_Joining_Group
Join Control
Jamo Short Name
Joining Type Non Joining
Line Break Alphabetic
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Vector Or Cross Product
NFKC Quick Check Yes
NFKD Quick Check Yes
Numeric Type None
Numeric Value not a number
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Pattern Syntax
Pattern White Space
Prepended Concatenation Mark
Quotation Mark
Regional Indicator
Sentence Break Other
Simple Case Folding Vector Or Cross Product
Script Extension
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Vertical Orientation R
Variation Selector
Word Break Other
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD