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.

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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 $\vecu$