Vector - General (Physical), Spatial Vector, Displacement Vector, Position Vector, Basis VectorMathematical Coordinate Representation

General (Physical)- Representation of a magnitude and direction. Representation may be graphical and/or mathematical. Anything that has a magnitude and a direction can be represented as a vector. Examples include displacement from a point, position (see below), velocity, force, electric field, magnetic field, thermal gradient, acceleration, etc. Compare descriptor.

Spatial Vector - A vector denoting the spatial relationship (distance and direction). It may be used to represent  the relation between two points in space or the displacement of a point in space or any other distance-direction concept . See also translation vector.

Given two points A and B, VectorAB.gif (917 bytes) is the vector with its base at A and tip at B. Its magnitude is the distance between A and B and its direction is in the direction   from A toward B.  Equivalent  vectors describe the same relationship between different sets of points. That is, if there is a point D which is  separated by the same distance and direction from C as  B  is from A, then VectorCD.gif (915 bytes) is equivalent to (the same as) the vector.

Displacement Vector - A   vector denoting the changing spatial relationship (distance and direction) of a point (real or virtual, physical or mathematical). See also translation vector.

Position Vector - The spatial vector to a given point from (relative to) another reference point such as the origin of a coordinate system.

Basis Vector - The spatial vectors that are used by a   coordinate system (cs) to describe all other spatial vectors in that system using coordinates.

Basis vectors  (usually referred to as i,j, and k) can have any dimensions such as millimeters or inches. The direction and distance from the origin (position vector) for an object (at point P)can be determined by a linear combination of i,j, and k (ai+b,j+ck), The coordinates for P  would be (a, b, c)

Coordinate Representation of a Vector