# Difference between revisions of "Vector"

From Glossary of Meteorology

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− | <div class="definition"><div class="short_definition">Any quantity, such as force, [[velocity]], or [[acceleration]], that has both magnitude and direction at each point in space, as opposed to a [[scalar]] that has magnitude only.</div><br/> <div class="paragraph">Such a quantity may be represented geometrically by an arrow of length proportional to its magnitude, pointing in the assigned direction. A unit vector is a vector of unit length; in particular, the three unit vectors along the positive ''x'', ''y'', and ''z'' axes of [[rectangular Cartesian coordinates]] are denoted, respectively, by '''i''', '''j''', and '''k'''. Any vector '''A''' can be represented in terms of its components ''a''<sub>1</sub>, ''a''<sub>2</sub>, and ''a''<sub>3</sub> along the coordinate axes ''x'', ''y'', and ''z'', respectively; for example, '''A''' = ''a''<sub>1</sub>'''i''' + ''a''<sub>2</sub>'''j''' + ''a''<sub>3</sub>'''k'''. A vector drawn from a fixed origin to a given point (''x'', ''y'', ''z'') is called a [[position vector]] and is usually symbolized by '''r'''; in rectangular Cartesian coordinates, <div class="display-formula"><blockquote>[[File:ams2001glos-Ve5.gif|link=|center|ams2001glos-Ve5]]</blockquote></div> Equations written in vector form are valid in any [[coordinate system]]. Mathematically, a vector is a single-row or single-column array of functions obeying certain laws of transformation. <br/>''See'' [[scalar product]], [[vector product]], [[Helmholtz's theorem]].</div><br/> </div> | + | <div class="definition"><div class="short_definition">Any quantity, such as force, [[velocity]], or [[acceleration]], that has both magnitude and direction at each point in space, as opposed to a [[scalar]] that has magnitude only.</div><br/> <div class="paragraph">Such a quantity may be represented geometrically by an arrow of length proportional to its magnitude, pointing in the assigned direction. A unit vector is a vector of unit length; in particular, the three unit vectors along the positive ''x'', ''y'', and ''z'' axes of [[rectangular Cartesian coordinates]] are denoted, respectively, by '''i''', '''j''', and '''k'''. Any vector '''A''' can be represented in terms of its components ''a''<sub>1</sub>, ''a''<sub>2</sub>, and ''a''<sub>3</sub> along the coordinate axes ''x'', ''y'', and ''z'', respectively; for example, '''A''' = ''a''<sub>1</sub>'''i''' + ''a''<sub>2</sub>'''j''' + ''a''<sub>3</sub>'''k'''. A vector drawn from a fixed origin to a given point (''x'', ''y'', ''z'') is called a [[position vector]] and is usually symbolized by '''r'''; in rectangular Cartesian coordinates, <div class="display-formula"><blockquote>[[File:ams2001glos-Ve5.gif|link=|center|ams2001glos-Ve5]]</blockquote></div> Equations written in vector form are valid in any [[coordinate system]]. Mathematically, a vector is a single-row or single-column array of functions obeying certain laws of transformation. <br/>''See'' [[scalar product|scalar product]], [[vector product]], [[Helmholtz's theorem]].</div><br/> </div> |

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## Latest revision as of 18:11, 25 April 2012

## vector

Any quantity, such as force, velocity, or acceleration, that has both magnitude and direction at each point in space, as opposed to a scalar that has magnitude only.

Such a quantity may be represented geometrically by an arrow of length proportional to its magnitude, pointing in the assigned direction. A unit vector is a vector of unit length; in particular, the three unit vectors along the positive Equations written in vector form are valid in any coordinate system. Mathematically, a vector is a single-row or single-column array of functions obeying certain laws of transformation.

*x*,*y*, and*z*axes of rectangular Cartesian coordinates are denoted, respectively, by**i**,**j**, and**k**. Any vector**A**can be represented in terms of its components*a*_{1},*a*_{2}, and*a*_{3}along the coordinate axes*x*,*y*, and*z*, respectively; for example,**A**=*a*_{1}**i**+*a*_{2}**j**+*a*_{3}**k**. A vector drawn from a fixed origin to a given point (*x*,*y*,*z*) is called a position vector and is usually symbolized by**r**; in rectangular Cartesian coordinates,*See*scalar product, vector product, Helmholtz's theorem.