Foot of Perpendicular from a Point to a Line

Foot of Perpendicular from a Point to a Line

For line:

$$\vec r=\vec a+\lambda\vec d$$

and point $$p$$ with position vector $$\vec p$$:

$$\lambda=\frac{(\vec p-\vec a)\cdot\vec d}{|\vec d|^2}$$

The foot is:

$$\vec h=\vec a+\lambda\vec d$$

Usage

- Used to find the perpendicular projection of a point onto a line.