Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 6C / c

For a plane reflection, the $n$ direction is reversed while $n^{\perp }$ is fixed. Thus $L=-1$, $\alpha =1$, and $\gamma =0$, equivalently

The map is a rotation about the $n$ axis exactly whenor explicitlyThese conditions make the axis fixed and the perpendicular-plane action length preserving; they are also necessary.