Reflection Matrix Proof

The video tutorial explains the concept of vector reflection using a mirror. It begins by introducing the vectors involved and the goal of deriving a formula to calculate the reflection. The tutorial then delves into the mathematical derivation, using the law of reflection and vector properties to establish equations. These equations are simplified to find the mirror matrix, which is used to calculate the reflection vector. The video also explores the mirror matrix in both 2D and 3D contexts, highlighting its dependence on the normal vector. Finally, it concludes by discussing variations of the reflection problem.

Discuss the implications of using unit vectors in the reflection calculations.

In what way does the mirror matrix depend on the normal vector?

Describe how the mirror matrix can be expressed using the angle of the mirror alpha.