projection of point

Let a line l be given in a Euclidean planeMathworldPlanetmath or space. The (orthogonalMathworldPlanetmathPlanetmath) projection of a P onto the line l is the point P of l at which the normal line of l passing through P intersects l. One says that P has been (orthogonally) projected onto the line l.


The projection of a set S of points onto the line l is defined to be the set of projection points of all points of S on l.

Especially, the projection of a PQ onto l is the line segmentMathworldPlanetmath PQ determined by the projection points P and Q of P and Q. If the length of PQ is a and the angle between the lines ( PQ and l is α, then the length p of its projection is

p=acosα. (1)

Remark.  As one speaks of the projections onto a line l, one can speak in the Euclidean space also of projections onto a plane τ.

Title projection of point
Canonical name ProjectionOfPoint
Date of creation 2013-03-22 17:09:50
Last modified on 2013-03-22 17:09:50
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 21
Author pahio (2872)
Entry type Definition
Classification msc 51N99
Synonym orthogonal projection
Related topic Projection
Related topic CompassAndStraightedgeConstructionOfPerpendicular
Related topic MeusniersTheorem
Defines project
Defines projection of line segment