# Vector Product

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Related to Vector Product: vector multiplication

## vector product

[′vek·tər ‚präd·əkt] (mathematics)

## 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