Two boats leave a harbor at the same time. BoatA cruises northwest at a rate of $18$ knots $($nautical miles per hour$).$ Boat B cruises north at a rate of $21$ knots.

Assume that $x-$axis points to the east and $y-$axis points to the north.

$($a$)$ Find the displacement vector from boat A to boat B half an hour later.

avec$(i)+$bvec$(j),$ where $a=$ and $b=$

$($b$)$ For the passengers in boat A $,$ what does the velocity of boat B appear to be$?$

cvec$(i)+$dvec$(j),$ where $c=$ and $d=$