# Projection of point on line

This calculator computes the coordinates of the orthogonal projection of a point M on a line in a 2 or 3 dimensional space.

## Projection of a point on a line in 2D or 3D space

This formula calculates the orthogonal projection of a point M on a Line L passing through point A and directed by vector `\vecu`.

M : the point to project

A : point of the Line L

u : Direction vector of Line L

P : projected point of M on Line L

`\vec(OP) = \vec(OA) + (\vec(AM)*\vecu)/|\vecu|^2 * \vecu`

`\vecu*\vecv` is the dot product of `\vecu` and `\vecv`

`|\vecu|` is the norm of vector `\vecu`

## See also

Matrix transformation Calculator

Line Calculator (2D)

Line Calculator (3D)

Vector projection Calculator

Coordinate Geometry Calculators

Geometry Calculators

Mathematics Calculators