The length of the arrow on a certain scale represents the magnitude of the vector and the head of the arrow, and gives the direction of the vector.

Let’s consider an example. Suppose an airplane is flying east with a speed of 500 km/h. To represent the speed of this plane, we first indicate the north south direction on the paper.

Second, we select a suitable scale, say 100 kilometers per hour represented by 1.0 cm, just as we do when drawing a geographical map. According to this scale, 500 km/h will be represented by a 5 cm line. We now draw a line 5c, of length parallel to the easterly direction, and place an arrowhead at A. These arrows represent the velocity vector of 500 km/h to the east. The length of this arrow represents the magnitude of the given vector on a selected scale and the arrowhead at A indicates the direction of the vector. So the line is called a representative line vector. The starting point O of the line is the tail, while the arrowhead is at the terminal point of the vector.

In the example above, the speed of the aircraft has been represented using the north-south and east directions. However, vectors are often represented by using three straight lines perpendicular to each other. One of these is called the x-axis, but we are limited to two lines. These two lines are called the reference axis. For example, a lawn mower is pulled with a force of 15 N acting at an angle of 30 with the ground level. In this example, the x-axis represents ground level and the line drawn at 30 with the x-axis gives the representative line for the force required.

It should be remembered that a representative line represents the given vector and can start from any point as long as its length and direction do not change. At some point, a vector is represented by two letters written at two ends of the representative line. In the example above, the force vector F–> can be represented by The arrow in indicates that the direction of this vector is from O to A.