Difference between revisions of "PerpendicularVector Command"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}}
{{command|vector-matrix}}
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;PerpendicularVector( <Line> )
;PerpendicularVector[Line]
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:Returns the perpendicular vector of the line.
:Returns the perpendicular vector of the line.
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:{{example|1=<div> Let <code><nowiki>Line((1, 4), (5, -3))</nowiki></code> be the line ''j''. <code><nowiki>PerpendicularVector(j)</nowiki></code> yields the perpendicular vector ''u=(7, 4)'' of the line ''j''.</div>}}
 
:{{note|1=A line with equation ''ax + by = c'' has the perpendicular vector ''(a, b)''.}}
 
:{{note|1=A line with equation ''ax + by = c'' has the perpendicular vector ''(a, b)''.}}
;PerpendicularVector[Segment]
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:Returns the perpendicular vector of the segment with the same length.  
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;PerpendicularVector( <Segment> )
; PerpendicularVector[Vector v]
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:Returns the perpendicular vector of the segment with the same length.
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:{{example|1=<div> Let <code><nowiki>Segment((3, 2), (14, 5))</nowiki></code> be the segment ''k''. <code><nowiki>PerpendicularVector(k)</nowiki></code> yields the perpendicular vector ''u=(-3, 11)'' of the segment ''k''.</div>}}
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; PerpendicularVector( <Vector> )
 
:Returns the perpendicular vector of the given vector.
 
:Returns the perpendicular vector of the given vector.
:{{note| A vector with coordinates ''(a, b)'' has the perpendicular vector ''(-b, a)''.}}
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:{{example|1=<div> Let <code><nowiki>Vector((-12, 8))</nowiki></code> be the vector ''u''. <code><nowiki>PerpendicularVector(u)</nowiki></code> yields the perpendicular vector ''v=(-8, -12)'' of the vector ''u''.</div>}}
==CAS Syntax==
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:{{note| In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] undefined variables are allowed as well.
; PerpendicularVector[Vector v]
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::{{example|<code><nowiki>PerpendicularVector((a, b))</nowiki></code> yields the vector ''{-b, a}''.}}
:Returns the perpendicular vector of the given vector.
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}}
:{{example|1=<div>
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:* <code><nowiki>PerpendicularVector[(3,2)]</nowiki></code> yields the vector ''{-2, 3}''.
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;PerpendicularVector( <Plane> )
:* <code><nowiki>PerpendicularVector[(a,b)]</nowiki></code> yields the vector ''{-b, a}''.</div>}}
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:Creates a vector orthogonal to the plane.
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:{{example|1=<div> <code><nowiki>PerpendicularVector(xOyPlane)</nowiki></code> yields the perpendicular vector ''u=(0, 0, 1)'' of the xOy plane.</div>}}
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{{note| 1=<div>See also [[UnitPerpendicularVector Command]].</div>}}

Latest revision as of 16:40, 29 September 2017


PerpendicularVector( <Line> )
Returns the perpendicular vector of the line.
Example:
Let Line((1, 4), (5, -3)) be the line j. PerpendicularVector(j) yields the perpendicular vector u=(7, 4) of the line j.
Note: A line with equation ax + by = c has the perpendicular vector (a, b).
PerpendicularVector( <Segment> )
Returns the perpendicular vector of the segment with the same length.
Example:
Let Segment((3, 2), (14, 5)) be the segment k. PerpendicularVector(k) yields the perpendicular vector u=(-3, 11) of the segment k.
PerpendicularVector( <Vector> )
Returns the perpendicular vector of the given vector.
Example:
Let Vector((-12, 8)) be the vector u. PerpendicularVector(u) yields the perpendicular vector v=(-8, -12) of the vector u.
Note: In the Menu view cas.svg CAS View undefined variables are allowed as well.
Example: PerpendicularVector((a, b)) yields the vector {-b, a}.
PerpendicularVector( <Plane> )
Creates a vector orthogonal to the plane.
Example:
PerpendicularVector(xOyPlane) yields the perpendicular vector u=(0, 0, 1) of the xOy plane.


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