Template:Vec/doc

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The {{vec}} mathematical formatting template typesets vectors using overscript [right arrow] notation (as an alternative to boldface notation, which is an option), unit vectors using [hat] notation, rays (i.e. half-lines) using overscript/underscript [either left arrow or right arrow] notation and lines using overscript/underscript [left-right arrow] notation. You may choose to obtain either HTML+CSS or LaTeX.

Usage

{{vec|vector/ray/line symbol|notation|format}}

where the first parameter (vector/ray/line symbol) is the base character

• e.g. E (default is A)

and the second parameter (notation) is among

• -> or o or o -> (overscript right arrow) (default)
• <- or o <- (overscript left arrow)
• <-> or o <-> (overscript left-right arrow)

• u or u -> (underscript right arrow)
• u <- (underscript left arrow)
• u <-> (underscript left-right arrow)

• b or bold (for vectors using bold notation, the base character being set in [non-italic] boldface)

• ^ or unit (for unit vectors using [hat] notation, the base character being set in italic boldface)

and the third parameter (format) is among (case insensitive)

• h or htm (default)
• t or tex

Notes

• Must be used inside the {{math}} template, since the fine tuning (tweaking) is optimized for it.
• The default for notation is set to match the LaTeX analogue \vec{A}: $\scriptstyle {\vec {x}}$.
• With arrow notation, the base character is automatically set in italic.
• With bold notation, the base character is automatically set in [non italic] bold.
• With unit vector [hat] notation, the base character is automatically set in italic boldface.

Examples

HTML+CSS examples

Notation	Code	Result	Code	Result	Code	Result
Default	{{math| {{vec|A}} |&&}}	A→	{{math| {{vec|A|o}} |&&}}	A→	{{math| {{vec|A|u}} |&&}}	A→
Right arrow	{{math| {{vec|v|->}} |&&}}	v→	{{math| {{vec|v|o ->}} |&&}}	v→	{{math| {{vec|v|u ->}} |&&}}	v→
Left arrow	{{math| {{vec|A|<-}} |&&}}	A←	{{math| {{vec|A|o <-}} |&&}}	A←	{{math| {{vec|A|u <-}} |&&}}	A←
Left-right arrow	{{math| {{vec|A|<->}} |&&}}	A↔	{{math| {{vec|A|o <->}} |&&}}	A↔	{{math| {{vec|A|u <->}} |&&}}	A↔

Notation	Code	Result	Code	Result	Code	Result
Boldface	{{math| {{vec|A|b}} |&&}}	A	{{math| {{vec|v|b}} |&&}}	v	{{math| {{vec|p|b}} |&&}}	p
"	{{math| {{vec|A|bold}} |&&}}	A	{{math| {{vec|v|bold}} |&&}}	v	{{math| {{vec|p|bold}} |&&}}	p
Unit vectors	{{math| {{vec|i|^}} |&&}}	𝚤̂	{{math| {{vec|j|^}} |&&}}	𝚥̂	{{math| {{vec|k|^}} |&&}}	k̂
"	{{math| {{vec|i|^}} |&}}	𝚤̂	{{math| {{vec|j|^}} |&}}	𝚥̂	{{math| {{vec|k|^}} |&}}	k̂
"	{{math| {{vec|e|^}}{{sub|1}} |&&}}	ê1	{{math| {{vec|e|^}}{{sub|2}} |&&}}	ê2	{{math| {{vec|e|^}}{{sub|3}} |&&}}	ê3
"	{{math| {{vec|i|unit}} |&&}}	𝚤̂	{{math| {{vec|j|unit}} |&&}}	𝚥̂	{{math| {{vec|k|unit}} |&&}}	k̂

TeX examples

Notation	Code	Result	Code	Result	Code	Result
Default	{{math| {{vec|A||tex}} |$$}}	${\begin{array}{l}\displaystyle {\vec {A}}\end{array}}$	{{math| {{vec|A|o|tex}} |$$}}	${\begin{array}{l}\displaystyle {\vec {A}}\end{array}}$	{{math| {{vec|A|u|tex}} |$$}}	${\begin{array}{l}\displaystyle {\underset {\rightarrow }{A}}\end{array}}$
Right arrow	{{math| {{vec|v|->|tex}} |$$}}	${\begin{array}{l}\displaystyle {\vec {v}}\end{array}}$	{{math| {{vec|v|o ->|tex}} |$$}}	${\begin{array}{l}\displaystyle {\vec {v}}\end{array}}$	{{math| {{vec|v|u ->|tex}} |$$}}	${\begin{array}{l}\displaystyle {\underset {\rightarrow }{v}}\end{array}}$
Left arrow	{{math| {{vec|A|<-|tex}} |$$}}	${\begin{array}{l}\displaystyle {\overset {\leftarrow }{A}}\end{array}}$	{{math| {{vec|A|o <-|tex}} |$$}}	${\begin{array}{l}\displaystyle {\overset {\leftarrow }{A}}\end{array}}$	{{math| {{vec|A|u <-|tex}} |$$}}	${\begin{array}{l}\displaystyle {\underset {\leftarrow }{A}}\end{array}}$
Left-right arrow	{{math| {{vec|A|<->|tex}} |$$}}	${\begin{array}{l}\displaystyle {\overset {\leftrightarrow }{A}}\end{array}}$	{{math| {{vec|A|o <->|tex}} |$$}}	${\begin{array}{l}\displaystyle {\overset {\leftrightarrow }{A}}\end{array}}$	{{math| {{vec|A|u <->|tex}} |$$}}	${\begin{array}{l}\displaystyle {\underset {\leftrightarrow }{A}}\end{array}}$

Notation	Code	Result	Code	Result	Code	Result
Boldface	{{math| {{vec|A|b|tex}} |$$}}	${\begin{array}{l}\displaystyle {\mathbf {A} }\end{array}}$	{{math| {{vec|v|b|tex}} |$$}}	${\begin{array}{l}\displaystyle {\mathbf {v} }\end{array}}$	{{math| {{vec|p|b|tex}} |$$}}	${\begin{array}{l}\displaystyle {\mathbf {p} }\end{array}}$
"	{{math| {{vec|A|bold|tex}} |$$}}	${\begin{array}{l}\displaystyle {\mathbf {A} }\end{array}}$	{{math| {{vec|v|bold|tex}} |$$}}	${\begin{array}{l}\displaystyle {\mathbf {v} }\end{array}}$	{{math| {{vec|p|bold|tex}} |$$}}	${\begin{array}{l}\displaystyle {\mathbf {p} }\end{array}}$
Unit vectors	{{math| {{vec|i|^|tex}} |$$}}	${\begin{array}{l}\displaystyle {\boldsymbol {\hat {\imath }}}\end{array}}$	{{math| {{vec|j|^|tex}} |$$}}	${\begin{array}{l}\displaystyle {\boldsymbol {\hat {\jmath }}}\end{array}}$	{{math| {{vec|k|^|tex}} |$$}}	${\begin{array}{l}\displaystyle {\boldsymbol {\hat {k}}}\end{array}}$
"	{{math| {{vec|i|^|tex}} |$}}	$\textstyle {\boldsymbol {\hat {\imath }}}$	{{math| {{vec|j|^|tex}} |$}}	$\textstyle {\boldsymbol {\hat {\jmath }}}$	{{math| {{vec|k|^|tex}} |$}}	$\textstyle {\boldsymbol {\hat {k}}}$
"	{{math| {{vec|e|^|tex}}{{sub|1|tex}} |$$}}	${\begin{array}{l}\displaystyle {{\boldsymbol {\hat {e}}}_{1}{\!\,\!}}\end{array}}$	{{math| {{vec|e|^|tex}}{{sub|2|tex}} |$$}}	${\begin{array}{l}\displaystyle {{\boldsymbol {\hat {e}}}_{2}{\!\,\!}}\end{array}}$	{{math| {{vec|e|^|tex}}{{sub|3|tex}} |$$}}	${\begin{array}{l}\displaystyle {{\boldsymbol {\hat {e}}}_{3}{\!\,\!}}\end{array}}$
"	{{math| {{vec|i|unit|tex}} |$$}}	${\begin{array}{l}\displaystyle {\boldsymbol {\hat {\imath }}}\end{array}}$	{{math| {{vec|j|unit|tex}} |$$}}	${\begin{array}{l}\displaystyle {\boldsymbol {\hat {\jmath }}}\end{array}}$	{{math| {{vec|k|unit|tex}} |$$}}	${\begin{array}{l}\displaystyle {\boldsymbol {\hat {k}}}\end{array}}$

Formulae examples

The code

Vorticity of a fluid with velocity field {{math|{{vec|u}}|&}}: inline as <!--
-->{{math|{{vec|{{Greek|omega}}}} {{=}} {{vec|{{op|nabla}}|b}} {{op|times}} {{vec|u}}|&}}, or display style

: {{math|{{vec|{{Greek|omega}}}} {{=}} {{vec|{{op|nabla}}|b}} {{op|times}} {{vec|u}}|&&}}

Tangential velocity in rigid body dynamics: inline as <!--
-->{{math|{{vec|v}} {{=}} {{vec|{{Greek|omega}}}} {{op|times}} {{vec|r}}|&}}, or display style

: {{math|{{vec|v}} {{=}} {{vec|{{Greek|omega}}}} {{op|times}} {{vec|r}}|&&}}

Rotating reference frame: inline as <!--
-->{{math|{{frac|''d''{{vec|A}}{{sym|prime}}|''dt''|HTM}} {{=}} 
{{frac|''d''{{vec|A}}|''dt''|HTM}} {{op|-}} {{vec|{{Greek|omega}}}} {{op|times}} {{vec|A}}|&}}, or display style

: {{math|{{frac|''d''{{vec|A}}{{sym|prime}}|''dt''|HTM}} {{=}} 
{{frac|''d''{{vec|A}}|''dt''|HTM}} {{op|-}} {{vec|{{Greek|omega}}}} {{op|times}} {{vec|A}}|&&}}

yields the HTML+CSS formatted

Vorticity of a fluid with velocity field 

u→

: inline as 

ω→ = ∇  ×  u→

, or display style

ω→ = ∇ × u→

Tangential velocity in rigid body dynamics: inline as 

v→ = ω→  ×  r→

, or display style

v→ = ω→ × r→

Rotating reference frame: inline as 

d'A→′ dt = d'A→ dt  −  ω→  ×  A→

, or display style

d'A→′ dt = d'A→ dt − ω→ × A→

while the code

Vorticity of a fluid with velocity field {{math|{{vec|u||tex}}|$}}: inline as <!--
-->{{math|{{vec|{{Greek|omega|tex}}||tex}} {{=}} {{vec|{{op|nabla|tex}}|b|tex}} {{op|times|tex}} {{vec|u||tex}}|$}}, or display style

: {{math|{{vec|{{Greek|omega|tex}}||tex}} {{=}} {{vec|{{op|nabla|tex}}|b|tex}} {{op|times|tex}} {{vec|u||tex}}|$$}}

Tangential velocity in rigid body dynamics: inline as <!--
-->{{math|{{vec|v||tex}} {{=}} {{vec|{{Greek|omega|tex}}||tex}} {{op|times|tex}} {{vec|r||tex}}|$}}, or display style

: {{math|{{vec|v||tex}} {{=}} {{vec|{{Greek|omega|tex}}||tex}} {{op|times|tex}} {{vec|r||tex}}|$$}}

Rotating reference frame: inline as <!--
-->{{math|{{frac|''d''{{vec|A||tex}}{{sym|prime|tex}}|''dt''|TEX}} {{=}} 
{{frac|''d''{{vec|A||tex}}|''dt''|TEX}} {{op|-|tex}} {{vec|{{Greek|omega|tex}}||tex}} {{op|times|tex}} {{vec|A||tex}}|$}}, or display style

: {{math|{{frac|''d''{{vec|A||tex}}{{sym|prime|tex}}|''dt''|TEX}} {{=}} 
{{frac|''d''{{vec|A||tex}}|''dt''|TEX}} {{op|-|tex}} {{vec|{{Greek|omega|tex}}||tex}} {{op|times|tex}} {{vec|A||tex}}|$$}}

yields the LaTeX formatted

Vorticity of a fluid with velocity field$\textstyle {\vec {u}}$: inline as$\textstyle {{\vec {\omega }}=\mathbf {{\nabla }\,} \,{\times }\,{\vec {u}}}$, or display style

${\begin{array}{l}\displaystyle {{\vec {\omega }}=\mathbf {{\nabla }\,} \,{\times }\,{\vec {u}}}\end{array}}$

Tangential velocity in rigid body dynamics: inline as$\textstyle {{\vec {v}}={\vec {\omega }}\,{\times }\,{\vec {r}}}$, or display style

${\begin{array}{l}\displaystyle {{\vec {v}}={\vec {\omega }}\,{\times }\,{\vec {r}}}\end{array}}$

Rotating reference frame: inline as$\textstyle {{\frac {d{\vec {A}}^{\prime }}{dt}}={\frac {d{\vec {A}}}{dt}}{\,}-{\,}{\vec {\omega }}\,{\times }\,{\vec {A}}}$, or display style

${\begin{array}{l}\displaystyle {{\frac {d{\vec {A}}^{\prime }}{dt}}={\frac {d{\vec {A}}}{dt}}-{\vec {\omega }}\,{\times }\,{\vec {A}}}\end{array}}$

See also

• {{overset}} and {{underset}} (for more general templates, allowing arbitrary characters and diacritics set over or under the base character)