A vector is represented by a directed line segment. The direction of the vector is indicated by an arrow pointing from the tail (initial point) to the head (terminal point) as shown in the figure below. If the tail is at point A and the head is at point B, the vector from A to B is written as

The length of the directed line segment shows its magnitude and the arrow head points the direction. The vector can also be represented by a single letter of the English alphabet (either small or capital) with arrow above it such as

(read as vector v). Sometimes we can also use the small letters in bold to represent vectors.

Example

What does each of the vectors in the following figure represent?

Solution

The unit of the magnitude of the vector tells us its type. For instance, N (Newton) is a unit of force and m/sec (meter per second) is a unit of speed.

Therefore, the first vector represents a force of 20N acting at an angle of 30° from the horizontal. (Note that the length of AB is proportional to the magnitude of the force.)

The second vector represents a velocity of 32 m/sec of a moving body in the direction of 60° from the horizontal. (Note that the length of the vector represents the magnitude 32 m/sec of the velocity and is drawn in proportion to it.)