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In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
It is formally defined as a directed line segment, or arrow, in a Euclidean space. [11] In pure mathematics , a vector is defined more generally as any element of a vector space . In this context, vectors are abstract entities which may or may not be characterized by a magnitude and a direction.
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat").
The direction in which the wave vector points must be distinguished from the "direction of wave propagation".The "direction of wave propagation" is the direction of a wave's energy flow, and the direction that a small wave packet will move, i.e. the direction of the group velocity.