Let $A\in SO(3)$. Then there exists a vector $v\in\mathbb{R}^3\setminus\{0\}$ such that $Av=v$. Moreover, the line $L=\operatorname{span}(v)$ is fixed pointwise by $A$, the orthogonal complement $L^\perp$ is invariant under $A$, and the restricted map $A|_{L^\perp}:L^\perp\to L^\perp$ is a planar rotation, with the identity allowed as rotation by angle $0$.