Difference between revisions of "UnitVector Command"
From GeoGebra Manual
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:{{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>}} | :{{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[ <Line> ] | ;UnitVector[ <Line> ] | ||
| − | :Yields the direction vector of the given line | + | :Yields the direction vector of the given line with length 1. |
:{{example|1=<div><code><nowiki>UnitVector[3x + 4y = 5]</nowiki></code> yields ''<math>\begin{pmatrix}0.8\\-0.6\end{pmatrix}</math>''.</div>}} | :{{example|1=<div><code><nowiki>UnitVector[3x + 4y = 5]</nowiki></code> yields ''<math>\begin{pmatrix}0.8\\-0.6\end{pmatrix}</math>''.</div>}} | ||
;UnitVector[ <Segment> ] | ;UnitVector[ <Segment> ] | ||
| − | :Yields the direction vector of the given segment | + | :Yields the direction vector of the given segment with length 1. |
| + | :{{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>}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
;UnitVector[ <Vector> ] | ;UnitVector[ <Vector> ] | ||
:Yields a vector with length 1, which has the same direction and orientation as the given vector. | :Yields a vector with length 1, which has the same direction and orientation as the given vector. | ||
| − | :{{example|1=<div><code><nowiki>UnitVector[(a, b)]</nowiki></code> yields '' | + | :{{example|1=<div><code><nowiki>UnitVector[(a, b)]</nowiki></code> yields ''(<math>\frac{a}{\sqrt{a^{2} + b^{2}}}</math>, <math>\frac{b}{\sqrt{a^{2} + b^{2}}}</math>)''.</div>}} |
| − | :{{example|1=<div><code><nowiki>UnitVector[(2, 4, 4)]</nowiki></code> yields '' | + | :{{example|1=<div><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>}} |
Revision as of 10:08, 21 May 2013
- 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}.
CAS Syntax
- UnitVector[ <Vector> ]
- Yields a vector with length 1, which has the same direction and orientation as the given vector.
- Example:
UnitVector[(a, b)]yields (\frac{a}{\sqrt{a^{2} + b^{2}}}, \frac{b}{\sqrt{a^{2} + b^{2}}}).
- Example:
UnitVector[(2, 4, 4)]yields (\frac{1}{3}, \frac{2}{3}, \frac{2}{3}).
