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A vector quantity is one which has magnitude and direction. For example, velocity is a vector quantity (whereas speed is a scalar quantity).

Vectors are commonly used to describe linear translations.

Addition of vectors is simple: you just add together the corresponding components of each vector; it is also easy to multiply a vector by a scalar - you simply multiply each component of the vector by the scalar. Multiplying vectors, however, is not so simple; there are different ways of multiplying vectors together - the two most commonly used are the scalar product (also called the dot-product) and the vector product (also called the cross-product).
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