Foot of Perpendicular from a Point to a Plane

Foot of Perpendicular from a Point to a Plane

For plane:

$$\vec r\cdot\vec n=d$$

and point with position vector $$\vec a$$, the foot $$\vec p$$ lies along the normal direction:

$$\vec p=\vec a-\frac{\vec a\cdot\vec n-d}{|\vec n|^2}\vec n$$

Usage

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