## Cross Product

In mathematics, the **cross product**, **vector product**, or **Gibbs' vector product** is a binary operation on two vectors in three-dimensional space. It results in a vector which is perpendicular to both of the vectors being multiplied and therefore normal to the plane containing them. It has many applications in mathematics, physics, and engineering.

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### Some articles on cross product:

**Cross Product**(disambiguation)

... The

**cross product**is a

**product**in vector algebra ...

**Cross product**may also refer to Seven-dimensional

**cross product**, a related

**product**in seven dimensions A

**product**in a Künneth theorem A crossed

**product**in von Neumann algebras A Cartesian ...

**Cross Product**- Rotations

... In three dimensions the

**cross product**is invariant under the group of the rotation group, SO(3), so the

**cross product**of x and y after they are rotated is the image of x × y under the rotation ... But this invariance is not true in seven dimensions that is, the

**cross product**is not invariant under the group of rotations in seven dimensions, SO(7) ...

**Cross Product**-

**Cross Product**(two Vectors)

... in some right-handed coordinate system using an orthonormal basis), their

**cross product**can be written as a determinant hence also using the Levi-Civita symbol, and more simply In Einstein notation ...

**Cross Product**- Coordinate Expressions

... To define a particular

**cross product**, an orthonormal basis {ej} may be selected and a multiplication table provided that determines all the

**products**{ei × ej} ... to five other unit vectors, allowing many choices for each

**cross product**... table from the one in the Introduction, leading to a different

**cross product**, is given with anticommutativity by More compactly this rule can be written as with i = 1...7 modulo 7 and the indices i, i + 1 and i + 3 ...

**Cross Product**- History

... Lagrange introduced the component form of both the dot and

**cross products**in order to study the tetrahedron in three dimensions ... In 1843 the Irish mathematical physicist Sir William Rowan Hamilton introduced the quaternion

**product**, and with it the terms "vector" and "scalar" ... u and v are vectors in R3, their quaternion

**product**can be summarized as ...

### Famous quotes containing the words product and/or cross:

“Labor is work that leaves no trace behind it when it is finished, or if it does, as in the case of the tilled field, this *product* of human activity requires still more labor, incessant, tireless labor, to maintain its identity as a “work” of man.”

—Mary McCarthy (1912–1989)

“We are no longer in a state of growth; we are in a state of excess. We are living in a society of excrescence.... The boil is growing out of control, recklessly at *cross* purposes with itself, its impacts multiplying as the causes disintegrate.”

—Jean Baudrillard (b. 1929)