Answer
Please see the figure attached.
${\bf{F}}\left( P \right) = \left( { - 2,1} \right)$
${\bf{F}}\left( Q \right) = \left( {1, - 1} \right)$
Work Step by Step
We have the vector field ${\bf{F}} = \left( { - y,x} \right)$.
The vector assigned to $P = \left( {1,2} \right)$ is
${\bf{F}}\left( P \right) = \left( { - 2,1} \right)$
The vector assigned to $Q = \left( { - 1, - 1} \right)$ is
${\bf{F}}\left( Q \right) = \left( {1, - 1} \right)$
Please see the figure attached.
