Austin buys a new moped he travel 3 km south and then 4 km east and then 3km north how far does he need to go to get back to where he started

The first thing to do is to define the origin of the coordinate system as the point at which the moped journey begins.
 Then, you must write the position vector:
 r = -3j + 4i + 3j
 Rewriting
 r = 4i
 To go back to where you started, you must go
 d = -4i
 That is to say, must travel a distance of 4Km to the west.
 Answer
 West, 4km.