ಟೆಂಪ್ಲೇಟು:Vec/doc ಇಗೆ ಮೂಲವನ್ನು ವಿಕ್ಷಿಸಿ

This template creates vectors using arrow notation in HTML, as an alternative to '''boldface'''. 

==Parameters==

The template has three parameters:

<ol>
<li>'''''Vector symbol''''': Insert the character, i.e. ''A'', Ω etc. Default is ''A''; to immediately show the template is in use, and prevent the arrow moving and overlapping text to one side.</li>
<li>'''''Arrow direction''''': Select one of ''left'', ''right'', or ''double'' for the arrows →, ←, or ↔ respectively. The default is ''right''.</li>
<li>'''''Arrow position''''': Select one of ''under'' or ''over'' to place the arrow over or under the character symbolizing the vector. The default is ''over''.</li>
</ol>

The defaults for 2 and 3 are set to match the LaTeX analogue of <code>\vec</code>: <math>\vec{A}</math>.

==Examples==

===No {{tl|math}}===

Illustration of all possibilities for italic ''A'':

{| class="wikitable"
|-
! 
! Default 
! Overarrow
! Underarrow
|-
! Default
|{{vec|''A''}}
|{{vec|''A''||over}}
|{{vec|''A''||under}}
|-
! Left
|{{vec|''A''|left}}
|{{vec|''A''|left|over}}
|{{vec|''A''|left|under}}
|-
! Right
|{{vec|''A''|right}}
|{{vec|''A''|right|over}}
|{{vec|''A''|right|under}}
|-
! Double
|{{vec|''A''|double}}
|{{vec|''A''|double|over}}
|{{vec|''A''|double|under}}
|-
|}

with code:

{| class="wikitable"
|-
! 
! Default 
! Overarrow
! Underarrow
|-
! Default
|<code><nowiki>{{vec|''A''}}</nowiki></code>
|<code><nowiki>{{vec|''A''||over}}</nowiki></code>
|<code><nowiki>{{vec|''A''||under}}</nowiki></code>
|-
! Left
|<code><nowiki>{{vec|''A''|left}}</nowiki></code>
|<code><nowiki>{{vec|''A''|left|over}}</nowiki></code>
|<code><nowiki>{{vec|''A''|left|under}}</nowiki></code>
|-
! Right
|<code><nowiki>{{vec|''A''|right}}</nowiki></code>
|<code><nowiki>{{vec|''A''|right|over}}</nowiki></code>
|<code><nowiki>{{vec|''A''|right|under}}</nowiki></code>
|-
! Double
|<code><nowiki>{{vec|''A''|double}}</nowiki></code>
|<code><nowiki>{{vec|''A''|double|over}}</nowiki></code>
|<code><nowiki>{{vec|''A''|double|under}}</nowiki></code>
|-
|}

Formulae:

[[Vorticity]] of a fluid with [[velocity field]] {{vec|''u''}}:

:{{vec|''ω''}} = {{vec|&nabla;}} × {{vec|''u''}}

Tangential [[velocity]] in [[rigid body dynamics]]:

:{{vec|''v''}} = {{vec|''ω''}} × {{vec|''r''}}

[[Rotating reference frame]]:

:{{frac|d{{vec|''A''&prime;}}|d''t''}} = {{frac|d{{vec|''A''}}|d''t''}} &minus; {{vec|''ω''}} × {{vec|''A''}}

:{{sfrac|d{{vec|''A''&prime;}}|d''t''}} = {{sfrac|d{{vec|''A''}}|d''t''}} &minus; {{vec|''ω''}} × {{vec|''A''}}

===Including {{tl|math}}===

Illustration of all possibilities for italic ''A'':

{| class="wikitable"
|-
! 
! Default 
! Overarrow
! Underarrow
|-
! Default
|{{math|{{vec|''A''}}}}
|{{math|{{vec|''A''||over}}}}
|{{math|{{vec|''A''||under}}}}
|-
! Left
|{{math|{{vec|''A''|left}}}}
|{{math|{{vec|''A''|left|over}}}}
|{{math|{{vec|''A''|left|under}}}}
|-
! Right
|{{math|{{vec|''A''|right}}}}
|{{math|{{vec|''A''|right|over}}}}
|{{math|{{vec|''A''|right|under}}}}
|-
! Double
|{{math|{{vec|''A''|double}}}}
|{{math|{{vec|''A''|double|over}}}}
|{{math|{{vec|''A''|double|under}}}}
|-
|}

with code:

{| class="wikitable"
|-
! 
! Default 
! Overarrow
! Underarrow
|-
! Default
|<code><nowiki>{{math|{{vec|''A''}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''||over}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''||under}}}}</nowiki></code>
|-
! Left
|<code><nowiki>{{math|{{vec|''A''|left}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''|left|over}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''|left|under}}}}</nowiki></code>
|-
! Right
|<code><nowiki>{{math|{{vec|''A''|right}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''|right|over}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''|right|under}}}}</nowiki></code>
|-
! Double
|<code><nowiki>{{math|{{vec|''A''|double}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''|double|over}}}}</nowiki></code>
|<code><nowiki>{{math|{{vec|''A''|double|under}}}}</nowiki></code>
|-
|}

Formulae:

[[Vorticity]] of a fluid with [[velocity field]] {{vec|''u''}}:

:{{math|{{vec|''ω''}} {{=}} {{vec|&nabla;}} × {{vec|''u''}}}}

Tangential [[velocity]] in [[rigid body dynamics]]:

:{{math|{{vec|''v''}} {{=}} {{vec|''ω''}} × {{vec|''r''}}}}

[[Rotating reference frame]]:

:{{math|{{frac|d{{vec|''A''&prime;}}|d''t''}} {{=}} {{frac|d{{vec|''A''}}|d''t''}} &minus; {{vec|''ω''}} × {{vec|''A''}}}}

:{{math|{{sfrac|d{{vec|''A''&prime;}}|d''t''}} {{=}} {{sfrac|d{{vec|''A''}}|d''t''}} &minus; {{vec|''ω''}} × {{vec|''A''}}}}

==See also==

*For [[quantum state]] vectors, see {{tl|braket}}.
*For more general templates, allowing arbitrary characters and diacritics set above or below one another, see {{tl|overset}} and {{tl|underset}}.

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