VECTORS

1. Scaler and Vectors

All physical quantities can be divided into two categories: Scaler and vectors.

SCALERS: Physical quantities which have only magnitude but no direction are called scalers. Mass, length, time, volume, speed, density, work, energy, power, temperature, specific heat, entropy, charge, electric current, electric potential, frequency etc. belong to this category.

Scaler quantity can be specified by a numerical value and a unit. For example, if one says that the average speed of a bicycle is 25 km/hr, 25 is the number(numerical value) and km/hr is the unit in which the speed has been expressed. This of course, does not say anything about the direction in which the bicycle is going. Scalers, being numbers, can be added algebraically.

VECTORS: Physical quantities, which has both magnitude as well as direction are called vectors. Velocity, acceleration, displacement, force, current density, electric and magnetic field, intensities etc belong to this category. Vector quantity can be specified by a unit, a numerical value and a statement about its direction. For example, if one says that the average velocity of a bicycle is 25 km/hr towards east, then this physical quantity has a numerical value25. a unit km/hr and a direction as east. Therefore, velocity is a vector.

The rule of ordinary algebra donot apply to vectors. For example, addition of two equal forces each of magnitude 2N can produce any resultant force from zero to 4N depending on direction of forces being added. In this chapter, we will define addition and multiplication rules for vectors and derive expressions for a resultant.