Vector Product

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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

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