Difference between revisions of "UnitVector Command"
From GeoGebra Manual
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;UnitVector[ <Vector> ] | ;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[v]</nowiki></code> | + | :{{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, with length 1 . | :Yields the direction vector of the given line, with length 1 . | ||
| − | :{{example|1=<div><code><nowiki>UnitVector[3x + 4y = 5]</nowiki></code> | + | :{{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, with length 1. | :Yields the direction vector of the given segment, with length 1. | ||
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: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 ''{<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[{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> | + | :{{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 13:05, 6 September 2011
- 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.
CAS Syntax
In CAS View only one syntax is allowed:
- 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}}.
