Consider the following cases: A man walks 200 metres across a field in a direction 45?E of S.
A ship steams on a course 30?E of N at a speed of 20 km/h.
The wind is blowing at 40 km/h from N.
Notice that each motion involves a physical quantity which consists of a magnitude and a specific direction. In order to have a physical description (representation) of the quantity, the notion of a directed line segment is introduced.
A directed line segment, denoted by or PQ, is a line segment PQ with the direction along the line segment from P to Q.
The directed line segment PQ consists of a magnitude (the length of PQ) and a direction as specified. These characteristics also apply to the physical quantities mentioned above.
Each of the above quantities can be represented by a directed line segment as follows: 1. The motion of the man is called a displacement which can be represented by the directed line segments as shown below.