The diagram below defines four vectors, A$,$ B$,$ C$,$ and $D.$ Each of the $16$ squares on the picture measures $3\mathrm{.}00$ m by $3\mathrm{.}00$ m $.$ All the vectors start and end at intersection points of the grid lines.

You happen to be a participant in the Survivor reality show, and this diagram is part of an individual challenge$-$win the challenge, and you're guaranteed immunity at the next Tribal Council. The challenge says, "travel $6$A $+7$B $+7$C $+4$D$."$

The starting point is the bottom left corner of the picture above, with to the right on the diagram being east, and up being north. Doing some quick calculations, you determine the resultant vector of the vector sum given above.

$($a$)$ What is the magnitude of the resultant vector?

m

$($b$)$ What is the angle between the resultant vector and due east? degrees

$($c$)$ In the second part of the challenge, you're given the following instruction.

Travel $6A+xB+9C+4D$

This results in no net east or west motion. How far north do you travel? Hint: first find $x.$

m