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A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued ...
Vector notation. Describing an arrow vector v by its coordinates x and y yields an isomorphism of vector spaces. In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1][2] which may be Euclidean vectors, or more generally, members of a vector space.
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. [1][2] It is typically formulated as the product of a unit of measurement and a vector numerical value (unitless), often a Euclidean vector with magnitude and direction. For example, a ...
Vector algebra relations. The following are important identities in vector algebra. Identities that only involve the magnitude of a vector and the dot product (scalar product) of two vectors A · B, apply to vectors in any dimension, while identities that use the cross product (vector product) A × B only apply in three dimensions, since the ...
Lists of vector identities. There are two lists of mathematical identities related to vectors: Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc. list of lists. Category:
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
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Vector algebra. In mathematics, vector algebra may mean: The operations of vector addition and scalar multiplication of a vector space. The algebraic operations in vector calculus (vector analysis) – including the dot and cross products of 3-dimensional Euclidean space. Algebra over a field – a vector space equipped with a bilinear product.