Ok!! Can we get a specific vector? Maybe using the matrix of map $\sigma_a$ ? (Wondering)
Printable View
The question only asks for a fixed vector.
We know now that we need a vector perpendicular to the line of reflection.
The line has an angle a with respect to the positive x-axis.
So $(\cos a,\,\sin a)$ is a directional vector along the line.
Can we find a vector perpendicular to it? (Wondering)