Vikram starts from his house facing North. He walks 4 km straight ahead, turns left and walks 3 km, turns left again and walks 7 km, and finally turns left and walks 3 km. Where is he now with respect to his house?

Take the house as the origin. Facing North he walks 4 km North. A left turn faces him West, and 3 km West takes him 3 km to the left of the starting line. The next left turn faces him South, and 7 km South leaves him 3 km below the starting level. The last left turn faces him East, and 3 km East cancels the earlier 3 km West. He is now directly below the house, that is 3 km South of it.