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<ref name=Teodorescu>{{Cite book |last=Teodorescu |first=Petre P. |url=https://books.google.com.br/books?id=k4H2AjWh9qQC&pg=PA5&dq=%2522free+vector%2522+bound+vector&hl=en&newbks=1&newbks_redir=0&sa=X&redir_esc=y |title=Mechanical Systems, Classical Models: Volume 1: Particle Mechanics |date=2007-06-06 |publisher=Springer Science & Business Media |isbn=978-1-4020-5442-6 |language=en}}</ref>
Bound vector quantities are formulated as a ''[[directed line segment]]'', with a definite initial point besides the magnitude and direction of the main vector.<ref name="a306"/><ref name="m813"/>
For example, a [[force]] on the [[Euclidean plane]] has two Cartesian components in SI unit of [[newtons]] and an accompanying two-dimensional position vector in meters, for a total of four numbers on the plane (and six in space).<ref name="p822">{{cite book | last=Merches | first=I. | last2=Radu | first2=D. | title=Analytical Mechanics: Solutions to Problems in Classical Physics | publisher=CRC Press | year=2014 | isbn=978-1-4822-3940-9 | url=https://books.google.com.br/books?id=e9XMBQAAQBAJ&pg=PA379 | access-date=2024-09-09 | page=379}}</ref><ref name="z733">{{cite book | last=Borisenko | first=A.I. | last2=Tarapov | first2=I.E. | last3=Silverman | first3=R.A. | title=Vector and Tensor Analysis with Applications | publisher=Dover Publications | series=Dover Books on Mathematics | year=2012 | isbn=978-0-486-13190-0 | url=https://books.google.com.br/books?id=8eO7AQAAQBAJ&pg=PA2 | access-date=2024-09-08 | page=2}}</ref><ref name=Teodorescu/>
A simpler example of a bound vector is the [[translation (geometry)|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 space, with all coordinates having the same unit.<ref name="p422">{{cite book | title=Differential Geometry: A Geometric Introduction | chapter=Appendix A. Linear Algebra from a Geometric Point of View | publisher=David W. Henderson | publication-place=Ithaca, NY | date=2013 | isbn=978-1-4297-9984-3 | doi=10.3792/euclid/9781429799843-13 | page=121–138}}</ref><ref name="w531"/>
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 [[Support (mathematics)|support]] or region of application; it can be freely translated with no consequences; a [[displacement vector]] is a prototypical example of free vector.
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