Scalar and Vector Quantities

We have learnt in previous posts that, in physics, quantities are properties or values that can be measured. Measurement is very important in science as it is usually a means of communication by scientists and engineers. These quantities are categorized as fundamental/basic quantities (length, mass, time, electric current etc.) and derived quantities (such as volume, area, density, force, pressure and so on).

However, these quantities can further be classified into two: Scalars and Vector quantities.

Scalar Quantities

Some of these physical quantities can only be expressed in numerical values, thus they can only be described by their size or magnitude. Such quantities that give numerical values only are scalar quantities. Examples are: Length/distance, mass, volume, time, density, speed, energy, temperature etc.

Scalar quantities can be defined as those physical quantities that have only magnitude or size but no direction. Hence they do not give a complete description.

For example, if the distance travelled by a car is 50km. this gives only the magnitude or numerical value of the distance travelled but it does not express the direction to which the car travelled. Similarly a temperature of 280K in the Kelvin scale has no direction but only a numerical value.

Vector Quantities

On the contrary, some physical quantities give a complete description by expressing both the numerical value/magnitude and also the direction of action. These quantities are known as vector quantities. Examples are: Force, velocity, displacement, momentum, weight, acceleration etc.

Vector quantities are defined as those quantities that have both the numerical value/magnitude and direction.

For example, a car travels 50km northwest. This implies that the distance travelled is 50km (magnitude) while the direction of travel is northwest. This is therefore the displacement of the car. Displacement is distance travelled in a specified direction.

Differences between scalar and vector quantities

•          Scalar quantities have only magnitude or size but no direction while vector quantities have both magnitude and direction.
•        Scalar can be represented by numerical values only but vectors are represented by both numerical values and an arrowhead to show its direction.
•       Scalars can be added by arithmetic methods only but vectors are added by geometric methods.
•      Examples of scalar quantities are: Length, distance, mass, volume, time, temperature etc.       Examples of vector quantities are: displacement, momentum, weight, acceleration etc.