Question

how to use compass directions to describe the direction of each vector?

Answer 1

Do you want to use polar coordinates, or Cartesian?

Answer 2

In polar coordinates, one part of the vector is the angle (it is usually measured CCW from the x axis, but could just as easily be measured clockwise from North, as on a compass). Of course the other is the magnitude (how long is the vector?).

In Cartesian coordinates, the vector can be measured as a distance in the north or south direction, plus a distance in the east or west direction. This is not unlike giving a vector as an (x,y) coordinate.