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The cross product with respect to a right-handed coordinate system. 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 ), and is denoted by the symbol .
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In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
In mathematics, the seven-dimensional cross product is a bilinear operation on vectors in seven-dimensional Euclidean space.It assigns to any two vectors a, b in a vector a × b also in . [1]
In the following properties, which result almost immediately from the definition of an inner product, x, y and z are arbitrary vectors, and a and b are arbitrary scalars. , = , =
In mathematics, the exterior algebra or Grassmann algebra of a vector space is an associative algebra that contains , which has a product, called exterior product or wedge product and denoted with , such that = for every vector in .
In mathematics, any vector space has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on , together with the vector space structure of pointwise addition and scalar multiplication by constants.