You walk 10 miles north, 20 miles south, and 5 miles north. Taking north to be the positive y direction, define a position vector that describes your position on the y-axis.

Considering north as positive Y axis

First 10 miles north means a positive 10 displacement along y direction

Second 20 miles south means a negative 20 displacement along y direction

Third 5 miles south means a positive 5 displacement along y direction

So total displacement = 10 - 20 + 5 = - 5 miles displacement

So position vector of the final position = - 5 j