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 … See more

In 1842, William Rowan Hamilton first described the algebra of quaternions and the non-commutative Hamilton product. In particular, when the Hamilton product of two vectors (that is, pure quaternions with zero scalar part) is performed, it results in a quaternion with a … See more

Geometric meaning
The magnitude of the cross product can be interpreted as the positive area of the parallelogram having a and b as sides (see Figure 1):
Indeed, one can also compute the volume V of a See more

The cross product has applications in various contexts. For example, it is used in computational geometry, physics and engineering. A non … See more

The cross product of two vectors a and b is defined only in three-dimensional space and is denoted by a × b. In physics and applied mathematics, the wedge notation a ∧ b is often used … See more

Coordinate notation
If (i, j, k) is a positively oriented orthonormal basis, the basis vectors satisfy the following equalities
which imply, by the anticommutativity of the cross product, that See more

Conversion to matrix multiplication
The vector cross product also can be expressed as the product of a skew-symmetric matrix and a vector:
The columns [a]×,i … See more