Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 3 / ii / Solution

A vector transforms as $x^{\prime a}=R^a{}_b{x}^b$. The matrix fixes $n$, preserves lengths and orientation, and rotates the perpendicular plane through $\theta$. It is a rotation by angle $\theta$ about the axis $n$, with orientation fixed by the epsilon-term convention.