Definitions

# Position vector

A position, location or radius vector is a vector which represents the position of an object in space in relation to an arbitrary reference point. The concept applies to two- or three-dimensional space. The term is also used as a means of deriving displacement by the spatial comparison of two or more position vectors and are usually 2- or, through hyperspace-based theories, 3-dimensional or N-dimensional if belonging to an N-dimensional Euclidean hyperspace.

## Other applications

• 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. Inertial 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.