# Projection of Point on a Plane

Projection of a point C having position vector $$\vec{C}$$ on any plane having normal vector $$\vec{A}$$ making a vector $$\vec{B}$$ with any point on the plane is given by following formula

$$\vec{P}= \vec{C} - (\frac{(\vec{A} \cdot \vec{B}) \vec{A} }{\vert \vec{A} \vert ^2})$$

In the above formula $$\vec{P}$$ is the point of projection. The length of the projection D (i.e. the distance of the point from the line) is given by the following formula

$$D = \frac{\vec{A}\cdot\vec{B}}{\vert \vec{A} \vert}$$

The above formula gives a signed distance values (i.e. the distance values can be negative or positive).