Brainlet CS undergrad, please help.
If I have a vector A, and B is A with X mirrored, and C is A with Y mirrored

$\vec{a} = ( a_{x} , a_{y})$
$\vec{b} = ( -a_{x} , a_{y})$
$\vec{c} = ( a_{x} , -a_{y})$
$<br /> det(\begin{bmatrix}<br /> -a_{x} &amp; a_{y} \\<br /> a_{x} &amp; -a_{y} \\<br /> \end{bmatrix}) = 0<br /> <br />$

Then B and C sit in the same line and they are always linearly dependant?
iow If I mirror 2 copies of a vector one in X axis and other in Y, they are in a line?
Is this true? If so, how is this relation called?