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We can understand any scientific explanation with the help of numerous physical quantities as each physical quantity signifies a distinct meaning which is significant in that context. Now the question arises: what is a physical quantity? According to the definition of a physical quantity it is a measurable and quantifiable physical property that contains unique information. Some examples of a physical quantity are length, time, velocity, etc.
A physical quantity is divided into two parts:
- Scalar.
- Vector.
Scalar quantity: Those physical quantities that indicate only in magnitude, not in the direction are known as a scalar quantity. Mass, length, speed, etc all are examples of scalar quantity as they are only expressed in magnitude and not in the direction
We can understand the scalar quantity clearly by solving a question.
- A person walks in the direction of north and stops after 10m then we move towards the east and again stop after 12m then walks 3m towards the west and finally 5m towards south to reach his office. To find out the magnitude and his displacement from his starting point.
Solution. As we know that displacement is a vector quantity so the man walks in positive and negative along an axis.
Assume Distance towards the north is positive and negative towards the south
10m – 5m = 5m
And let the distance covered by man in east is positive and in west it is negative
– 3m + 12m = 9m
We use Pythagoras theorem to find displacement:
- D2 = 92 + 52
- D2 = 81 + 25
- D= 10.3
- D= 10.30m
Vector quantity – Alike from scalar quantity vector not only required magnitude but it also required direction so any physical quantity which consists of both the direction and magnitude is known as a vector quantity. For example, displacement, velocity, acceleration, etc contains both magnitude and direction. But it does not mean that every quantity which has both magnitude and direction is the vector, for example pressure and electric current have both magnitude and direction but still they are not vectored as they failed to follow the laws of vector addition.
From the above definition, we can conclude that scalar quantity is different from vector quantity whereas scalar quantities have direction but scalar quantity does not have any direction and because of this characteristic a scalar can only indicate only in one dimension, whereas vector quantity can be represented in multiple directions.
Scalar quantity
It has only magnitude but it does not have any direction, it is one dimensional. If there is any change that occurred in scalar quantity then the effect of that change is also seen in magnitude. Regardless of direction, scalar quantity can’t be resolved as it has the same value. By using different arithmetic rules scalar quantities can be divided, multiply, added, and subtracted. We can describe the scalar quantity in two ways
- By a number.
- By a suitable unit.
Vector quantity
It contains both magnitudes as well as directions. It has multiple dimensions; it can be one, two, or three. If there is any change occurring in the vector then that change is seen as either a change in magnitude or change in direction or sometimes in both. It can be resolved in any direction by using the sine or cosine of an adjacent angle. By using different arithmetic rules scalar quantity cannot be divided, multiply, added, and subtracted
We can describe the vector quantity in three ways –
- By number.
- By using a suitable unit.
- By using a certain direction.
Conclusion
It is very important to know how scalar and vectors are used in our daily life. Take an example of sports we play in our daily life routine like cricket, football or baseball. The vector is used by the players when they throw the ball in any particular direction with an angle and in designing a roller coaster. So if there is any change in either its magnitude or direction even a small change then the vector is also changed and let’s assume you go for a long trip of 50 km in 5 hours so your speed is 10km/hr So it is a scalar quantity.
