vector product

vector productc = a x b

vector product

n. A vector c, depending on two other vectors a and b, whose magnitude is the product of the magnitude of a, the magnitude of b, and the sine of the angle between a and b. Its direction is perpendicular to the plane through a and b and oriented so that a right-handed rotation about it carries a into b through an angle not greater than 180°. The notation for c is c = a × b. Also called cross product.

vector product

n (Mathematics) the product of two vectors that is a pseudovector, whose magnitude is the product of the magnitudes of the given vectors and the sine of the angle between them. Its axis is perpendicular to the plane of the given vectors. Written: A × B or A ∧ B. Also called: cross product Compare scalar product

cross′ prod`uct

n. a vector perpendicular to two given vectors and having magnitude equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. Also called vector product. [1925–30]

Thesaurus

Noun

vector product - a vector that is the product of two other vectorscross productvector - a variable quantity that can be resolved into components

Translations

Vector Product

vector product

[′vek·tər ‚präd·əkt] (mathematics) cross product

Vector Product

The vector product of vector a and vector b is the vector denoted by [a, b] and defined as follows: (1) the length of vector [a, b] is equal to the product of the lengths of vectors a and b and the sine of the angle φ between them (the angle between a and b which is less than or equal to π is used); (2) vector [a, b] is perpendicular to both vectors a and b; and (3) the set of three vectors a, b, and [a, b], in accordance with its spatial orientation, always forms either a right-handed or left-handed set. The vector product is widely used in geometry, mechanics, and physics; for example, the moment of a force F, applied to a point M with reference to a point O, is the vector product

REFERENCE

Il’in, V. A., and E. G. Pozniak. Analiticheskaia geometriia. Moscow, 1968.

E. G. POZNIAK

vector product

vector product

vector product

cross′ prod`uct

Vector Product

vector product

Vector Product

REFERENCE

vector product

Synonyms for vector product

noun a vector that is the product of two other vectors

Synonyms

Related Words