In 1835 Giusto Bellavitis introduced the idea of equipollent directed line segments $${\displaystyle AB\bumpeq CD}$$ which resulted in the concept of a vector as an equivalence class of … See more

The two polar coordinates of a point in a plane may be considered as a two dimensional vector. Such a vector consists of a magnitude (or length) and a direction (or angle). The magnitude, typically represented as r, is the distance from a starting point, the See more

A spherical vector is another method for extending the concept of polar vectors into three dimensions. It is akin to an arrow in the spherical coordinate system. A spherical vector is specified by a magnitude, an azimuth angle, and a zenith angle. The … See more

Vector notation is used with calculus through the Nabla operator: $${\displaystyle \mathbf {i} {\frac {\partial }{\partial x}}+\mathbf {j} {\frac {\partial }{\partial y}}+\mathbf {k} {\frac {\partial }{\partial z}}}$$ With a scalar function f, the gradient See more

Given a Cartesian coordinate system, a vector may be specified by its Cartesian coordinates.
Tuple notation
A vector v in n-dimensional real coordinate space can be specified using a tuple (ordered list) of … See more

A cylindrical vector is an extension of the concept of polar coordinates into three dimensions. It is akin to an arrow in the cylindrical coordinate system. A cylindrical vector is specified by … See more

In any given vector space, the operations of vector addition and scalar multiplication are defined. Normed vector spaces also define an operation known as the norm (or determination of … See more