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scalar multiplication

mathematics

Learn about this topic in these articles:

vectors

  • vector mathematics
    In mechanics: Vectors

    …may be multiplied by a scalar. Thus, for example, the vector 2A has the same direction as A but is twice as long. If the scalar has dimensions, the resulting vector still has the same direction as the original one, but the two cannot be compared in magnitude. For example,…

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scalar, a physical quantity that is completely described by its magnitude. Examples of scalars are volume, density, speed, energy, mass, and time. Other quantities, such as force and velocity, have both magnitude and direction and are called vectors.

Scalars are described by real numbers that are usually but not necessarily positive. The work done on a particle by a force, for example, is a negative number when the particle moves in a direction opposite to that in which the force acts, such as when the frictional force slows down a moving body. Scalars can be manipulated by the ordinary laws of algebra.

The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Erik Gregersen.