A vector is a mathematical and physical concept representing a quantity that has both magnitude (size or length) and direction. Geometrically, it can be visualized as a directed line segment or an arrow pointing from one point to another, where the length corresponds to the magnitude and the arrowhead indicates the direction
. Vectors are used to describe physical quantities such as displacement, velocity, force, and acceleration, which cannot be fully described by a single number (a scalar) because they require direction as well as magnitude
. For example, velocity includes both speed and the direction of motion. In mathematics, vectors are elements of vector spaces, which are sets equipped with operations of vector addition and scalar multiplication that satisfy specific axioms. This generalizes the concept of vectors beyond geometry to include tuples and other abstract entities
. Vectors can be added together and scaled by numbers (scalars), and these operations follow algebraic rules like commutativity and associativity. This makes vectors fundamental in fields such as physics, engineering, and computer graphics
. In summary, a vector is an entity characterized by both magnitude and direction, essential for representing directional quantities in science and mathematics
