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 a b. 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.
Seen & Heard
What made you look up vector operations? Please tell us what you were reading, watching or discussing that led you here.