Reflection of a Point in a Plane Using Vectors

Reflection of a Point in a Plane Using Vectors

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

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

the reflected point has position vector:

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

Usage

- Used for reflection problems when the plane is given in vector form.