In mathematics, a quantity characterized by magnitude and direction. Some physical and geometric quantities, called scalars, can be fully defined by a single number specifying their magnitude in suitable units of measure (e.g., mass in grams, temperature in degrees, time in seconds). Quantities like velocity, force, and displacement must be specified by a magnitude and a direction. These are vectors. A vector quantity can be visualized as an arrow drawn in a specific direction, whose length is equal to the magnitude of the quantity represented. A two-dimensional vector is specified by two coordinates, a three-dimensional vector by three coordinates, and so on. Vector analysis is a branch of mathematics that explores the utility of this type of representation and defines the ways such quantities may be combined. See also vector operations.

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