Multiplication by $A$ rotates the $(x,y)$ components by $\theta$ counterclockwise when viewed from positive $z$ toward the origin, leaving $z$ unchanged. It is a <proper rotation> about the $z$ axis, with <determinant> $+1$. Multiplication by $B$ sends $(x,y,z)$ to $(x,y,-z)$: it is a <reflection> in the $xy$ plane, with <determinant> $-1$. Neither operation changes a <vector>'s Euclidean <norm>.

Solution

Past exam of the mathematical methods I course of the University of Oxford / 2022 / 5 / i / Solution

 Solution (source code)