Difference between revisions of "PerpendicularVector Command"

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:Returns the perpendicular vector of the given vector.
 
:Returns the perpendicular vector of the given vector.
 
:{{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>}}
 
:{{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>}}
:{{note| A vector with coordinates ''(a, b)'' has the perpendicular vector ''(-b, a)''.}}
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:{{note| In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] undefined variables are allowed as well.
 +
::{{example|<code><nowiki>PerpendicularVector[(a, b)]</nowiki></code> yields the vector ''{-b, a}''.}}
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}}
  
 
;PerpendicularVector[ <Plane> ]  
 
;PerpendicularVector[ <Plane> ]  
 
:Creates a vector orthogonal to the plane.
 
:Creates a vector orthogonal to the plane.
 
:{{example|1=<div> <code><nowiki>PerpendicularVector[ xOyPlane ]</nowiki></code> yields the perpendicular vector ''u=(0, 0, 1)'' of the xOy plane.</div>}}
 
:{{example|1=<div> <code><nowiki>PerpendicularVector[ xOyPlane ]</nowiki></code> yields the perpendicular vector ''u=(0, 0, 1)'' of the xOy plane.</div>}}
 
==CAS Syntax==
 
; PerpendicularVector[ <Vector> ]
 
:Returns the perpendicular vector of the given vector.
 
:{{example|1=<div>
 
:* <code><nowiki>PerpendicularVector[(3, 2)]</nowiki></code> yields the vector ''{-2, 3}''.
 
:* <code><nowiki>PerpendicularVector[(a, b)]</nowiki></code> yields the vector ''{-b, a}''.</div>}}
 
  
 
{{note| 1=<div>See also [[UnitPerpendicularVector Command]].</div>}}
 
{{note| 1=<div>See also [[UnitPerpendicularVector Command]].</div>}}

Revision as of 14:08, 1 October 2015


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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