# Show the properties of σ

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• February 12th, 2020, 20:07
mathmari
Re: Show the properties of σ
Quote:

Originally Posted by Klaas van Aarsen
Yep. (Nod)

Ok!! Can we get a specific vector? Maybe using the matrix of map $\sigma_a$ ? (Wondering)
• February 13th, 2020, 04:33
Klaas van Aarsen
Re: Show the properties of σ
Quote:

Originally Posted by mathmari
Ok!! Can we get a specific vector? Maybe using the matrix of map $\sigma_a$ ? (Wondering)

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)
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