Difference between revisions of "UnitVector Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
{{command|vector-matrix}}
 
{{command|vector-matrix}}
; UnitVector[Vector]: Yields a vector with length 1, which has the same direction and orientation as the given 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=<code>UnitVector[{2, 4, 4}]</code> returns ''{<math>\frac{1}{3}</math>, <math>\frac{2}{3}</math>, <math>\frac{2}{3}</math>}''.}}
+
: {{Example|1=Let ''v=<math>\begin{pmatrix}3\\4\end{pmatrix}</math>. <code>UnitVector[v]</code> returns ''<math>\begin{pmatrix}0.6\\0.8\end{pmatrix}</math>''.}}
 
; UnitVector[Line]: Yields the direction vector of the given line, with length 1 .
 
; UnitVector[Line]: Yields the direction vector of the given line, with length 1 .
 +
: {{Example|1=<code>UnitVector[3x + 4y = 5]</code> returns ''<math>\begin{pmatrix}0.8\\-0.6\end{pmatrix}</math>''.}}
 
; UnitVector[Segment]: Yields the direction vector of the given segment, with length 1
 
; UnitVector[Segment]: Yields the direction vector of the given segment, with length 1
 +
 
==CAS Syntax==
 
==CAS Syntax==
 
In [[CAS View]] only one syntax is allowed:
 
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.
 
; UnitVector[Vector]: Yields a vector with length 1, which has the same direction and orientation as the given vector.
 
: {{Example|1=<code>UnitVector[{a,b}]</code> returns ''{<math>\frac{a}{\sqrt{a²+b²&#125;}</math>,<math>\frac{b}{\sqrt{a²+b²&#125;}</math>}''.}}
 
: {{Example|1=<code>UnitVector[{a,b}]</code> returns ''{<math>\frac{a}{\sqrt{a²+b²&#125;}</math>,<math>\frac{b}{\sqrt{a²+b²&#125;}</math>}''.}}

Revision as of 10:37, 23 August 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] returns \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] returns \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}] returns {\frac{a}{\sqrt{a²+b²}},\frac{b}{\sqrt{a²+b²}}}.
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