A man walks 5 km towards the north, then turns right and walks 3 km, then turns right again and walks 5 km, and finally turns left and walks 4 km. In which direction is he facing now?
Show Hint
Plot the walk on an x-y grid with north as up, and apply the standard clockwise-for-right, counter-clockwise-for-left turn rule at each step to track the final facing direction.
Step 1: Set up a coordinate system with the starting point at the origin $(0,0)$ and north as the $+y$ direction, east as $+x$. Step 2: Walk 5 km north: new position $(0,5)$, still facing north. Step 3: A right turn while facing north points the man east (clockwise from N is E). Walking 3 km east: position becomes $(0+3,\,5)=(3,5)$, now facing east. Step 4: A right turn while facing east points him south (clockwise from E is S). Walking 5 km south: position becomes $(3,\,5-5)=(3,0)$, now facing south. Step 5: A left turn while facing south points him east (counter-clockwise from S is E). Walking 4 km east: position becomes $(3+4,\,0)=(7,0)$. Step 6: His final facing direction after this last left turn is east, and his last leg of movement itself was also along the east direction, confirming the result. Correct option: East
