Difference between revisions of "UnitPerpendicularVector Command"
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| − | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}} |
| − | {{command|cas=true|vector-matrix}} | + | ;UnitPerpendicularVector( <Line>) |
| − | ;UnitPerpendicularVector | ||
:Returns the perpendicular vector with length 1 of the given line. | :Returns the perpendicular vector with length 1 of the given line. | ||
| − | :{{example|1=<div><code><nowiki>UnitPerpendicularVector | + | :{{example|1=<div><code><nowiki>UnitPerpendicularVector(3x + 4y = 5)</nowiki></code> yields ''<math>\begin{pmatrix}0.6\\0.8\end{pmatrix}</math>''.</div>}} |
| − | ;UnitPerpendicularVector | + | ;UnitPerpendicularVector( <Segment> ) |
:Returns the perpendicular vector with length 1 of the given segment. | :Returns the perpendicular vector with length 1 of the given segment. | ||
| − | ;UnitPerpendicularVector | + | :{{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>}} |
| − | :Returns the perpendicular vector with length 1 of the given vector. The vector must be | + | ;UnitPerpendicularVector( <Vector> ) |
| − | :{{example|1=<div>Let v=<math>\begin{pmatrix}3\\4\end{pmatrix}</math>. <code><nowiki>UnitPerpendicularVector | + | :Returns the perpendicular vector with length 1 of the given vector. The vector must be defined first. |
| + | :{{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>}} | ||
| + | {{note|In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] vectors with undefined variables are also valid input. | ||
| + | :{{example|<div><code><nowiki>UnitPerpendicularVector((a, b))</nowiki></code> yields ''(<math>\frac{-b}{\sqrt{a^{2} + b^{2}}}</math>,<math>\frac{a}{\sqrt{a^{2} + b^{2}}}</math>)''.</div>}} | ||
| + | }} | ||
| + | |||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;UnitPerpendicularVector | + | ;UnitPerpendicularVector( <Plane> ) |
| − | : | + | :Creates a unit vector orthogonal to the plane. |
| − | + | ||
| + | {{note| 1=<div>See also [[PerpendicularVector Command]].</div>}} | ||
Latest revision as of 17:46, 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 
CAS View vectors with undefined variables are also valid input.
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.
Note:
See also PerpendicularVector Command.
