$(14)$ A small plane flies $30\mathrm{.}0$ km in a direction $45$ north of east $($Vector A$),$ and then flies $45\mathrm{.}0$ km in a direction $30$ south of west $($Vector B$).$

a$.$ Create the vectors A and $B,$ in terms of i and $j,$ assuming East is the x direction, and $N$ is the y direction.

b$.$ Draw the approximate airplane path for each leg, and show a final angle relative to the eastern direction $($positive x axis$).$

c$.$ Find the total distance that the plane covers from the starting point at O $,$ and the angle of the path from the East axis to the final position.

d$.$ If the vector $C=A+B,$ find the magnitude of $C.$

Distrotal $$ km

$C=$ km

Angle between $C$ and x $-$axis $$