Difference between revisions of "UnitVector Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}} | ||
| − | ;UnitVector | + | ;UnitVector( <Vector> ) |
:Yields a vector with length 1, which has the same direction and orientation as the given vector. The vector must be defined first. | :Yields a vector with length 1, which has the same direction and orientation as the given vector. The vector must be defined first. | ||
| − | :{{example|1=<div>Let ''v=<math>\begin{pmatrix}3\\4\end{pmatrix}</math>''. <code><nowiki>UnitVector | + | :{{example|1=<div>Let ''v=<math>\begin{pmatrix}3\\4\end{pmatrix}</math>''. <code><nowiki>UnitVector(v)</nowiki></code> yields ''<math>\begin{pmatrix}0.6\\0.8\end{pmatrix}</math>''.</div>}} |
| − | ;UnitVector | + | ;UnitVector( <Line> ) |
:Yields the direction vector of the given line with length 1. | :Yields the direction vector of the given line with length 1. | ||
| − | :{{example|1=<div><code><nowiki>UnitVector | + | :{{example|1=<div><code><nowiki>UnitVector(3x + 4y = 5)</nowiki></code> yields ''<math>\begin{pmatrix}0.8\\-0.6\end{pmatrix}</math>''.</div>}} |
| − | ;UnitVector | + | ;UnitVector( <Segment> ) |
:Yields the direction vector of the given segment with length 1. | :Yields the direction vector of the given segment with length 1. | ||
| − | :{{example|1=<div>Let <code><nowiki>s = Segment | + | :{{example|1=<div>Let <code><nowiki>s = Segment((1,1),(4,5))</nowiki></code>. <div><code><nowiki>UnitVector(s)</nowiki></code> yields ''<math>\begin{pmatrix}0.6\\0.8\end{pmatrix}</math>''.</div></div>}} |
{{hint|1= | {{hint|1= | ||
In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] three-dimensional vectors and vectors with undefined variables are also valid inputs. | In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] three-dimensional vectors and vectors with undefined variables are also valid inputs. | ||
:{{examples|1=<div> | :{{examples|1=<div> | ||
| − | :*<code><nowiki>UnitVector | + | :*<code><nowiki>UnitVector((a, b))</nowiki></code> yields ''(<math>\frac{a}{\sqrt{a a + b b}}</math>, <math>\frac{b}{\sqrt{a a + b b}}</math>)''. |
| − | :* <code><nowiki>UnitVector | + | :* <code><nowiki>UnitVector((2, 4, 4))</nowiki></code> yields ''(<math>\frac{1}{3}</math>, <math>\frac{2}{3}</math>, <math>\frac{2}{3}</math>)''.</div>}} |
}} | }} | ||
Latest revision as of 17:45, 29 September 2017
- UnitVector( <Vector> )
- Yields a vector with length 1, which has the same direction and orientation as the given vector. The vector must be defined first.
- Example:Let v=\begin{pmatrix}3\\4\end{pmatrix}.
UnitVector(v)yields \begin{pmatrix}0.6\\0.8\end{pmatrix}.
- UnitVector( <Line> )
- Yields the direction vector of the given line with length 1.
- Example:
UnitVector(3x + 4y = 5)yields \begin{pmatrix}0.8\\-0.6\end{pmatrix}.
- UnitVector( <Segment> )
- Yields the direction vector of the given segment with length 1.
- Example:Let
s = Segment((1,1),(4,5)).UnitVector(s)yields \begin{pmatrix}0.6\\0.8\end{pmatrix}.
Hint: In the 
CAS View three-dimensional vectors and vectors with undefined variables are also valid inputs.
- Examples:
UnitVector((a, b))yields (\frac{a}{\sqrt{a a + b b}}, \frac{b}{\sqrt{a a + b b}}).UnitVector((2, 4, 4))yields (\frac{1}{3}, \frac{2}{3}, \frac{2}{3}).
