$1.$ Two planes take off from the same airport at the same time. Airplane $\backslash ($ A $\backslash )$ has an air speed of $500$ mph and a bearing of $\backslash (280^\{\backslash$circ$\}\backslash )($note that in navigation, directors or bearings are measured clock$-$wise from North$)$ and airplane B has an air speed of $600$ mph and a bearing of $\backslash (15^\{\backslash$circ$\}\backslash ).($There is no wind during the flights.$)$

a$.$ After $2$ hours, what is the displacement vector from airplane A to airplane B $?$ Write using unit vectors with East as $\backslash (+$x $\backslash )$ and North as $\backslash (+$y $\backslash ).$