Trickier this time: you walk 5 km north, 2 km east, 3 km south. How far from start, and in which direction?
Vector approach
Net north = 5 − 3 = 2 km. Net east = 2 km. Distance = √(2² + 2²) = √8 ≈ 2.83 km. Bearing: northeast (45°).
Vectors decompose any walk into north/south and east/west. Add the components separately, then Pythagoras.