cross product - meaning and definition. What is cross product
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What (who) is cross product - definition


Cross product         
  • [[Standard basis]] vectors ('''i''', '''j''', '''k''', also denoted '''e'''<sub>1</sub>, '''e'''<sub>2</sub>, '''e'''<sub>3</sub>) and [[vector component]]s of '''a''' ('''a'''<sub>x</sub>, '''a'''<sub>y</sub>, '''a'''<sub>z</sub>, also denoted '''a'''<sub>1</sub>, '''a'''<sub>2</sub>, '''a'''<sub>3</sub>)
  • '''a''' × '''b'''}} (vertical, in purple) changes as the angle between the vectors '''a''' (blue) and '''b''' (red) changes. The cross product is always orthogonal to both vectors, and has magnitude zero when the vectors are parallel and maximum magnitude ‖'''a'''‖‖'''b'''‖ when they are orthogonal.
  • isbn=978-0-07-161545-7}}</ref>
  • Figure 1. The area of a parallelogram as the magnitude of a cross product
  • Cross product [[scalar multiplication]]. '''Left:''' Decomposition of '''b''' into components parallel and perpendicular to '''a'''. Right: Scaling of the perpendicular components by a positive real number ''r'' (if negative, '''b''' and the cross product are reversed).
  • rejection]]. The triple product is in the plane and is rotated as shown.
  • The cross product in relation to the exterior product. In red are the orthogonal [[unit vector]], and the "parallel" unit bivector.
  • Figure 2. Three vectors defining a parallelepiped
  • Finding the direction of the cross product by the [[right-hand rule]]
  • According to [[Sarrus's rule]], the [[determinant]] of a 3×3 matrix involves multiplications between matrix elements identified by crossed diagonals
MATHEMATICAL OPERATION ON TWO VECTORS
Vector product; Vector cross product; Evaluating cross products; Cross Product; Evaluating cross-products; Cross products; Sarrus's scheme; Cross-product; Crossproduct; Vector Product; ⨯; Vectorial product; Cross product matrix; Three-dimensional cross product; Ccw test; Xyzzy (mnemonic); Generalizations of the 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), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them.
https://en.wikipedia.org/wiki/Cross_product
cross product         
  • [[Standard basis]] vectors ('''i''', '''j''', '''k''', also denoted '''e'''<sub>1</sub>, '''e'''<sub>2</sub>, '''e'''<sub>3</sub>) and [[vector component]]s of '''a''' ('''a'''<sub>x</sub>, '''a'''<sub>y</sub>, '''a'''<sub>z</sub>, also denoted '''a'''<sub>1</sub>, '''a'''<sub>2</sub>, '''a'''<sub>3</sub>)
  • '''a''' × '''b'''}} (vertical, in purple) changes as the angle between the vectors '''a''' (blue) and '''b''' (red) changes. The cross product is always orthogonal to both vectors, and has magnitude zero when the vectors are parallel and maximum magnitude ‖'''a'''‖‖'''b'''‖ when they are orthogonal.
  • isbn=978-0-07-161545-7}}</ref>
  • Figure 1. The area of a parallelogram as the magnitude of a cross product
  • Cross product [[scalar multiplication]]. '''Left:''' Decomposition of '''b''' into components parallel and perpendicular to '''a'''. Right: Scaling of the perpendicular components by a positive real number ''r'' (if negative, '''b''' and the cross product are reversed).
  • rejection]]. The triple product is in the plane and is rotated as shown.
  • The cross product in relation to the exterior product. In red are the orthogonal [[unit vector]], and the "parallel" unit bivector.
  • Figure 2. Three vectors defining a parallelepiped
  • Finding the direction of the cross product by the [[right-hand rule]]
  • According to [[Sarrus's rule]], the [[determinant]] of a 3×3 matrix involves multiplications between matrix elements identified by crossed diagonals
MATHEMATICAL OPERATION ON TWO VECTORS
Vector product; Vector cross product; Evaluating cross products; Cross Product; Evaluating cross-products; Cross products; Sarrus's scheme; Cross-product; Crossproduct; Vector Product; ⨯; Vectorial product; Cross product matrix; Three-dimensional cross product; Ccw test; Xyzzy (mnemonic); Generalizations of the cross product
¦ noun another term for vector product.
vector product         
  • [[Standard basis]] vectors ('''i''', '''j''', '''k''', also denoted '''e'''<sub>1</sub>, '''e'''<sub>2</sub>, '''e'''<sub>3</sub>) and [[vector component]]s of '''a''' ('''a'''<sub>x</sub>, '''a'''<sub>y</sub>, '''a'''<sub>z</sub>, also denoted '''a'''<sub>1</sub>, '''a'''<sub>2</sub>, '''a'''<sub>3</sub>)
  • '''a''' × '''b'''}} (vertical, in purple) changes as the angle between the vectors '''a''' (blue) and '''b''' (red) changes. The cross product is always orthogonal to both vectors, and has magnitude zero when the vectors are parallel and maximum magnitude ‖'''a'''‖‖'''b'''‖ when they are orthogonal.
  • isbn=978-0-07-161545-7}}</ref>
  • Figure 1. The area of a parallelogram as the magnitude of a cross product
  • Cross product [[scalar multiplication]]. '''Left:''' Decomposition of '''b''' into components parallel and perpendicular to '''a'''. Right: Scaling of the perpendicular components by a positive real number ''r'' (if negative, '''b''' and the cross product are reversed).
  • rejection]]. The triple product is in the plane and is rotated as shown.
  • The cross product in relation to the exterior product. In red are the orthogonal [[unit vector]], and the "parallel" unit bivector.
  • Figure 2. Three vectors defining a parallelepiped
  • Finding the direction of the cross product by the [[right-hand rule]]
  • According to [[Sarrus's rule]], the [[determinant]] of a 3×3 matrix involves multiplications between matrix elements identified by crossed diagonals
MATHEMATICAL OPERATION ON TWO VECTORS
Vector product; Vector cross product; Evaluating cross products; Cross Product; Evaluating cross-products; Cross products; Sarrus's scheme; Cross-product; Crossproduct; Vector Product; ⨯; Vectorial product; Cross product matrix; Three-dimensional cross product; Ccw test; Xyzzy (mnemonic); Generalizations of the cross product
¦ noun Mathematics the product of two vectors which is itself a vector at right angles to both the original vectors and equal to the product of their magnitudes and the sine of the angle between them (written as a . b).
Examples of use of cross product
1. Prior to joining Nomura Investment Banking in early 2005, he worked for BNP and BNP Paribas in Bahrain from 1''6 where he held a number of roles including responsibility for marketing and product development of equity derivative, cross–product business development for institutional and private clients across the GCC as well as pioneering a range of Shariah–compliant equity derivative products, according to EIIB Managing Director John Weguelin.
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