![]() Vectors can be added to other vectors according to vector algebra. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector ) is a geometric object that has magnitude (or length) and direction. The term vector is generally not used for elements of these vectors spaces, and is generally reserved for geometric vectors, tuples, and elements of unspecified vector spaces (for example, when discussing general properties of vector spaces). Many vector spaces are considered in mathematics, such as extension field, polynomial rings, algebras and function spaces. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is called a coordinate vector space. The term vector is also used, in some contexts, for tuples, which are finite sequences of numbers of a fixed length.īoth geometric vectors and tuples can be added and scaled, and these vector operations led to the concept of a vector space, which is a set equipped with a vector addition and a scalar multiplication that satisfy some axioms generalizing the main properties of operations on the above sorts of vectors. Such quantities are represented by geometric vectors in the same way as distances, masses and time are represented by real numbers. ![]() ![]() Historically, vectors were introduced in geometry and physics (typically in mechanics) for quantities that have both a magnitude and a direction, such as displacements, forces and velocity. In mathematics and physics, vector is a term that refers colloquially to some quantities that cannot be expressed by a single number (a scalar), or to elements of some vector spaces. ![]()
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