Difference between revisions of "UnitVector Command"

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}).

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}}
-{{command|cas=true|vector-matrix}}
+;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.
-:{{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, 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> 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, with length 1.
+:Yields the direction vector of the given segment with length 1.
-==CAS Syntax==
+:{{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>}}
-;UnitVector[ <Vector> ]
-:Yields a vector with length 1, which has the same direction and orientation as the given vector.
+{{hint|1=
-:{{example|1=<div><code><nowiki>UnitVector[(a, b)]</nowiki></code> yields ''{<math>\frac{a}{\sqrt{a^{2} + b^{2}&#125;}</math>, <math>\frac{b}{\sqrt{a^{2} + b^{2}&#125;}</math>}''.</div>}}
+In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] three-dimensional vectors and vectors with undefined variables are also valid inputs.
-:{{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>}}
+:{{examples|1=<div>
+:*<code><nowiki>UnitVector((a, b))</nowiki></code> yields ''(<math>\frac{a}{\sqrt{a a + b b&#125;}</math>, <math>\frac{b}{\sqrt{a a + b b&#125;}</math>)''.
+:* <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>}}
+}}

Difference between revisions of "UnitVector Command"

Latest revision as of 17:45, 29 September 2017

UnitVector

Command Categories (All commands)