A car is $2\mathrm{.}3$ km west of a traffic light at t $=0$ and $4\mathrm{.}6$ km east of the light at t $=7\mathrm{.}5$ min.

Assume the origin of the coordinate system is the light and the positive x$-$direction is eastward. $($Express your answers in vector form.$)$ $$

$($a$)$ What are the car's position vectors $($in km$)$ at these two times?

$($b$)$ What is the car's displacement $($in km$)$ between $0$ min and $7\mathrm{.}5$ min?