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Extension of the laws of elementary algebra to vectors. They include addition, subtraction, and three types of multiplication. The sum of two vectors is a third vector, represented as the diagonal of the parallelogram constructed with the two original vectors as sides. When a vector is multiplied by a positive scalar (i.e., number), its magnitude is multiplied by the scalar and its direction remains unchanged (if the scalar is negative, the direction is reversed). The multiplication of a vector a by another vector b leads to the dot product, written a · b, and the cross product, written ab. The dot product, also called the scalar product, is a scalar real number equal to the product of the lengths of vectors a (
This entry comes from Encyclopædia Britannica Concise. For the full entry on vector operations, visit Britannica.com.
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