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>
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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|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 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 a1, a2, and a3 along the coordinate axes x, y, and z, respectively; for example, A = a1i + a2j + a3k. 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,
ams2001glos-Ve5
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.
See scalar product, vector product, Helmholtz's theorem.