vector

Any quantity, such as force, velocity, or acceleration, that has both magnitude and direction at each point in space, as opposed to a scalar that has magnitude only.

Such a quantity may be represented geometrically by an arrow of length proportional to its magnitude, pointing in the assigned direction. A unit vector is a vector of unit length; in particular, the three unit vectors along the positive x, y, and z axes of rectangular Cartesian coordinates are denoted, respectively, by i, j, and k. Any vector A can be represented in terms of its components a₁, a₂, and a₃ along the coordinate axes x, y, and z, respectively; for example, A = a₁i + a₂j + a₃k. A vector drawn from a fixed origin to a given point (x, y, z) is called a position vector and is usually symbolized by r; in rectangular Cartesian coordinates,

Equations written in vector form are valid in any coordinate system. Mathematically, a vector is a single-row or single-column array of functions obeying certain laws of transformation.
See scalar product, vector product, Helmholtz's theorem.

A coordinate system in which the locations of points in space are expressed by reference to three planes, called coordinate planes, no two of which are parallel.