Certain physical quantities are completely described by a numerical value alone and are added according to the ordinary rules of algebra. As an example, the mass of a system is described by saying that it is 10 kg. If two bodies one having a mass of 10 kg and other 5 kg are added to make a composite system, the total mass of the system becomes
10 kg + 5 kg = 15 kg.
Such quantities are called Scalars.
The certain description of certain physical quantities requires a numerical value as well as direction in space. Velocity is an example of this kind. The magnitude of velocity tells us how fast a particle is, but description of velocity becomes complete only when the direction of velocity is also described. We can describe the direction by a line with an arrow showing the direction of velocity.
Such quantities are called Vectors.
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