# Representation of a Vector

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

Let us consider an example. Suppose an aeroplane flies towards east with a velocity of 500 km / h. To represent the velocity of this aeroplane we first indicate north south direction on the paper.

Secondly, we select a suitable scale, say 100 kilometer per hour being represented by 1.0 cm, just as we do while drawing a geographical map. According to this scale, 500 km / h will be represented by 5 cm line. Now we draw a line 5c, in length parallel to east direction, and put an arrowhead at A. This arrows represent by the velocity vector of 500 km / h toward east. The length of this arrow represent the magnitude of the given vector on a selected scale and arrow-head at A indicates the direction of the vector. So the line is called representative line vector. The initial point O of the line is the tail, while the arrow -head is at the terminal point of the vector.

In the above example, the velocity of the aeroplane has been represented by using north-South and east direction. However vectors are often represented by using any three straight lines mutually perpendicular to each other. One of these is named as x-axis, but we shell restrict ourselves to two lines. Such two lines are called reference axis. For example, a grass mover is pulled with a force of 15 N acting at an angle of 30 with the ground level. In this example x-axis represents the ground level and line drawn at 30 with x-axis gives the representative line of the required force.

It must be remembered that a representative line represent the given vector and it may start from any point provided its length and direction is not changed. Some time a vector is represented by two letters written at two extremities of representative line. In the above example, the force vector F -> can be represented by The arrow on indicates that the direction of this vector is from O to A.