A position vector is a vector used to describe the spatial position of a point relative to a reference point called the origin (of the space). It is also called radius vector.

Position vectors are usually 2- or 3-dimensional, but could also be N-dimensional if belonging to an N-dimensional Euclidean hyperspace.

In linear algebra, a position vector can be expressed as a linear combination of basis vectors.

The kinematic movement of a point mass can be described by a position vector field P(t) which depends on a scalar time parameter t.

In physics, moving position vectors are used in mechanics and dynamics to keep track of the positions of particles, point masses, or rigid objects.

In differential geometry, position vector fields are used to describe continuous and differentiable space curves, in which case the independent parameter need not be time, but can be (e.g.) arc length of the curve.