Contents
Studying Physics Topics can lead to exciting new discoveries and technological advancements.
What are the Differences Between Scalar and Vector?
Definition of Scalar and Vector Quantities
Physical quantities, used in science and technology are broadly classified into two groups, scalar quantities and vector quantities.
Scalar quantities:
Definition: A scalar quantity is a physical quantity having only magnitude but no direction.
Physical quantities like length, mass, time, relative density, energy, temperature, etc. are fully described by their magnitudes. These quantities do not have any direction. These are examples of scalar quantities.
Scalar:
Definition: Any number, that has a real magnitude only but no direction, is called a scalar.
Essentially, any real number—like 8, -2, \(\frac{1}{4}\), \(\sqrt{3}\) etc. is a scalar.
Naturally, if an appropriate unit is added to a scalar, it becomes a scalar quantity.
Example:
- The distance of a railway station is 10 km from my residence.
- It takes me 30 minutes (time) to reach school from my home.
In all the above examples we can see that a scalar quantity is completely expressed by a real number and a unit and thus have a complete information about the quantities.
Mathematical operations of scalars follow simple algebraic rules.
Vector quantities:
Definition: A vector quantity is defined as a physical quantity, having both magnitude and direction.
For physical quantities like displacement, velocity, acceleration, force, etc. the magnitude does not define the quantity fully. If we express the position of our school by saying that it is 4 km away from my residence then this statement is incomplete. The school cannot be located until we say that it is 4 km towards west from my residence. Thus position is a vector quantity. A statement such as ‘the bus stop is 200 m from where one is standing’ may not be useful until a direction is specified, like 200 m east.
Vector:
Definition: Any number, that has a real magnitude as well as a direction, is called a vector.
A vector quantity is expressed by a real number, a unit and a specific direction.
Example:
Velocity of a particle 10 m ᐧ s-1 towards east. If the unit is omitted, we get a vector. In this example, the vector is ‘10 towards east
5 towards south, -8 downwards, \(\frac{1}{2}\) along north-west, 2\(\sqrt{2}\) from south-west, etc. are the examples of vectors. Obviously, the vector ‘-8 downwards’ is identical to the vector ‘8 upwards’. If an appropriate unit is added to a vector, it becomes a vector quantity.
Differences between scalar and vector quantities:
| Scalar Quantities | Vector Quantities |
| 1. Physical quantities having only magnitude but no direction. | 1. Physical Quantities having both magnitude and direction. |
| 2. They can be added, subtracted, multipled and divided according to the simple rules of algebra. | 2. They can be added, subtracted and multiplied according to the rules of vector algebra. The division of a vector by another vector is not a valid operation in vector algebra. |
| 3. Multiplication of two scalars results into a scalar. | 3. Multiplication of two vectors may either be a scalar or vector. |
It is to be noted that scalars and vectors are mathematical elements only. After all mathematical operations, a proper unit must be added to the final result to obtain a meaningful physical quantity.