Difference between revisions of "PerpendicularVector Command"

Revision as of 11:15, 10 August 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: A vector with coordinates (a, b) has the perpendicular 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.

PerpendicularVector[ <Vector> ]

Returns the perpendicular vector of the given vector.

Example:

Note:

@@ Line 8: / Line 8: @@
 :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.