The PositionVector procedure constructs a position Vector, one of the principal data structures of the Vector Calculus package.

The call PositionVector(comps, c) returns a position Vector in a Cartesian enveloping space with components interpreted using the corresponding transformations from c coordinates to Cartesian coordinates.

If no coordinate system argument is present, the components of the position Vector are interpreted in the current coordinate system (see SetCoordinates).

The position Vector is a Cartesian Vector rooted at the origin, and has no mathematical meaning in non-Cartesian coordinates.

The c parameter specifies the coordinate system in which the components are interpreted; they will be transformed into Cartesian coordinates.

For more information about coordinate systems supported by VectorCalculus, see VectorCalculus,Coordinates.

If comps has indeterminates representing parameters, the position Vector serves to represent a curve or a surface.

To differentiate a curve or a surface specified via a position Vector, use diff.

To evaluate a curve or a surface given by a position Vector, use eval.

To evaluate a vector field along a curve or a surface given by a position Vector, use evalVF.

A curve or surface given by a position Vector can be plotted using PlotPositionVector.

The position Vector is displayed in column notation in the same manner as rooted Vectors are, as a position Vector can be interpreted as a Vector that is (always) rooted at the Cartesian origin.

A position Vector cannot be mapped to a basis different than Cartesian coordinates.  In order to see how the same position Vector would be described in other coordinate systems, use GetPVDescription.

Standard binary operations between position Vectors like +/-,*, Dot Product, Cross Product are defined.

Binary operations between position Vectors and vector fields, free Vectors or rooted Vectors are not defined; however, a position Vector can be converted to a free Vector in Cartesian coordinates via ConvertVector.

For details on the differences between position Vectors, rooted Vectors and free Vectors, see VectorCalculus,Details.