A vector is something that mathematicians and engineers use to represent or calculate a force that has direction. The vector will show the direction of the force and the size of the force as well. Sometimes vectors are represented by arrows, with length or thickness of the arrow representing force, and direction representing direction. Sometimes vectors are represented by sets of numbers.

Often vectors are used in spacecraft navigation. The engineers know where they want to go and use vectors to figure out what direction to thrust in to go there.


A Vector is a quantity possessing both magnitude and direction, represented by an arrow the direction of which indicates the direction of the quantity and the length of which is proportional to the magnitude.

Examples of vector quantitiee include displacement, velocity, acceleration, and force. Each of these quantities are unique in that a full description of the quantity demands that both a magnitude and a direction are listed. For example, suppose your teacher tells you “A bag of gold is located outside the classroom. To find it, displace yourself 20 meters.” This statement may provide yourself enough information to pique your interest; yet, there is not enough information included in the statement to find the bag of gold. The displacement required to find the bag of gold has not been fully described. On the other hand, suppose your teacher tells you “A bag of gold is located outside the classroom. To find it, displace yourself from the center of the classroom door 20 meters in a direction 30 degrees to the west of north.” This statement now provides a complete description of the displacement vector – it lists both magnitude (20 meters) and direction (30 degrees to the west of north) relative to a reference or starting position (the center of the classroom door). Vector quantities are not fully described unless both magnitude and direction are listed.


Vector quantities are often represented by scaled vector diagram. Vector diagrams depict a vector by use of an arrow drawn to scale in a specific direction.

The vector diagram depicts a displacement vector. Observe that there are several characteristics of this diagram that make it an appropriately drawn vector diagram.

  • a scale is clearly listed
  • a vector arrow (with arrowhead) is drawn in a specified direction. The vector arrow has a head and a tail.
  • the magnitude and direction of the vector is clearly labeled. In this case, the diagram shows the magnitude is 20 m and the direction is (30 degrees West of North).