Scalar & Vector Quantities

Scalar Quantities

Scalar quantities are quantities in which the magnitude is stated, but the direction is either not applicable or not specified.


  • Length
  • Volume
  • Mass
  • Speed

Vector Quantities

Vector quantities are quantities in which both the magnitude and the direction must be stated.


  • Force
  • Velocity
  • Displacement
  • Acceleration

It does not make sense to say that you’re applying a force of 10 N on a box without stating the direction. The force can be directed anywhere. Hence, you need to specify which direction the force is applied: 10 N in the horizontal direction on a box.

There will be more about how to differentiate speed, displacement, velocity and acceleration in the later chapter.

Worked Examples

Example 1

Which one of the following groups contains only vector quantities?

  1. force, work, energy
  2. displacement, momentum, acceleration
  3. power, energy, time
  4. momentum, mass, velocity
Click here to show/hide answer

Vector quantities: Force, displacement, momentum, velocity, acceleration

Scalar quantities: Work, energy, power, time, mass

Answer: 2

Example 2

Which of the following are vectors and which are not: force, temperature, the volume of water in a can, the ratings of a TV show, the height of a building, the velocity of a sports car, the age of the Universe?

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Only force and velocity are vectors. None of the other quantities requires a direction to be described.

Example 3

Can the magnitude of a vector have a negative value?

Click here to show/hide answer

No, the magnitude of a vector is always positive. A minus sign in a vector only indicates direction, not magnitude.

Example 4

Is it possible to add a vector quantity to a scalar quantity? Explain.

Click here to show/hide answer

Addition of a vector to a scalar is not defined.

Back To Measurement Of Physical Quantities (O Level Physics)

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