Difference between revisions of "PerpendicularVector Command"
From GeoGebra Manual
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| − | ;PerpendicularVector[Line] | + | |
| − | :Returns the perpendicular vector of the line. | + | ;PerpendicularVector[ <Line> ] |
| + | :Returns the perpendicular vector of the line. | ||
| + | :{{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] | + | |
| − | :Returns the perpendicular vector of the segment with the same length. | + | ;PerpendicularVector[ <Segment> ] |
| − | ; PerpendicularVector[Vector | + | :Returns the perpendicular vector of the segment with the same length. |
| + | :{{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>}} | ||
| + | |||
| + | ; PerpendicularVector[ <Vector> ] | ||
: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>}} | ||
:{{note| A vector with coordinates ''(a, b)'' has the perpendicular vector ''(-b, a)''.}} | :{{note| A vector with coordinates ''(a, b)'' has the perpendicular vector ''(-b, a)''.}} | ||
| + | |||
| + | |||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ; PerpendicularVector[Vector | + | ; PerpendicularVector[ <Vector> ] |
:Returns the perpendicular vector of the given vector. | :Returns the perpendicular vector of the given vector. | ||
:{{example|1=<div> | :{{example|1=<div> | ||
:* <code><nowiki>PerpendicularVector[(3, 2)]</nowiki></code> yields the vector ''{-2, 3}''. | :* <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>}} | :* <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 11:35, 10 July 2013
- 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: A vector with coordinates (a, b) has the perpendicular vector (-b, a).
CAS Syntax
- PerpendicularVector[ <Vector> ]
- Returns the perpendicular vector of the given vector.
- Example:
PerpendicularVector[(3, 2)]yields the vector {-2, 3}.PerpendicularVector[(a, b)]yields the vector {-b, a}.
Note:
See also UnitPerpendicularVector Command.
