Difference between revisions of "UnitPerpendicularVector Command"

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<noinclude>{{Manual Page}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}}
; UnitPerpendicularVector[Line]: Returns the perpendicular vector with length 1 of the given line.  
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;UnitPerpendicularVector( <Line>)
; UnitPerpendicularVector[Vector]: Returns the perpendicular vector with length 1 of the given vector.
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:Returns the perpendicular vector with length 1 of the given line.
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:{{example|1=<div><code><nowiki>UnitPerpendicularVector(3x + 4y = 5)</nowiki></code> yields ''<math>\begin{pmatrix}0.6\\0.8\end{pmatrix}</math>''.</div>}}
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;UnitPerpendicularVector( <Segment> )
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:Returns the perpendicular vector with length 1 of the given segment.
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:{{example|1=<div>Let <code><nowiki>s = Segment((1,1), (4,5))</nowiki></code>.<div><code><nowiki>UnitPerpendicularVector(s)</nowiki></code> yields ''<math>\begin{pmatrix}-0.8\\0.6\end{pmatrix}</math>''.</div></div>}}
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;UnitPerpendicularVector( <Vector> )
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:Returns the perpendicular vector with length 1 of the given vector. The vector must be defined first.
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:{{example|1=<div>Let v=<math>\begin{pmatrix}3\\4\end{pmatrix}</math>. <code><nowiki>UnitPerpendicularVector(v)</nowiki></code> yields ''<math>\begin{pmatrix}-0.8\\0.6\end{pmatrix}</math>''.</div>}}
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{{note|In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] vectors with undefined variables are also valid input.
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:{{example|<div><code><nowiki>UnitPerpendicularVector((a, b))</nowiki></code> yields ''(<math>\frac{-b}{\sqrt{a^{2} + b^{2}&#125;}</math>,<math>\frac{a}{\sqrt{a^{2} + b^{2}&#125;}</math>)''.</div>}}
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}}
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==CAS Syntax==
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;UnitPerpendicularVector( <Plane> )
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:Creates a unit vector orthogonal to the plane.
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{{note| 1=<div>See also [[PerpendicularVector Command]].</div>}}

Latest revision as of 16:46, 29 September 2017


UnitPerpendicularVector( <Line>)
Returns the perpendicular vector with length 1 of the given line.
Example:
UnitPerpendicularVector(3x + 4y = 5) yields \begin{pmatrix}0.6\\0.8\end{pmatrix}.
UnitPerpendicularVector( <Segment> )
Returns the perpendicular vector with length 1 of the given segment.
Example:
Let s = Segment((1,1), (4,5)).
UnitPerpendicularVector(s) yields \begin{pmatrix}-0.8\\0.6\end{pmatrix}.
UnitPerpendicularVector( <Vector> )
Returns the perpendicular vector with length 1 of the given vector. The vector must be defined first.
Example:
Let v=\begin{pmatrix}3\\4\end{pmatrix}. UnitPerpendicularVector(v) yields \begin{pmatrix}-0.8\\0.6\end{pmatrix}.
Note: In the Menu view cas.svg CAS View vectors with undefined variables are also valid input.
Example:
UnitPerpendicularVector((a, b)) yields (\frac{-b}{\sqrt{a^{2} + b^{2}}},\frac{a}{\sqrt{a^{2} + b^{2}}}).

CAS Syntax

UnitPerpendicularVector( <Plane> )
Creates a unit vector orthogonal to the plane.
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