Bound vector

In physics and engineering, particularly in mechanics, a physical vector may be endowed with additional structure compared to a geometrical vector. A bound vector is defined as the combination of an ordinary vector quantity and a point of application or point of action. Bound vector quantities are formulated as a directed line segment, with a definite initial point besides the magnitude and direction of the main vector. For example, a force on the Euclidean plane has two Cartesian components in SI unit of newtons (describing the magnitude and direction of the force) and an accompanying two-dimensional position vector in meters (describing the point of application of the force), for a total of four numbers on the plane (and six in space). A simpler example of a bound vector is the translation vector from an initial point to an end point; in this case, the bound vector is an ordered pair of points in the same position space, with all coordinates having the same quantity dimension and unit (length and meters). A sliding vector is the combination of an ordinary vector quantity and a line of application or line of action, over which the vector quantity can be translated (without rotations). A free vector is a vector quantity having an undefined point or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector.