The physical quantity that has only magnitude and no direction is scalar. A scalar quantity is a onedimensional quantity because it does not have any direction to make it two or threedimensional. Scalar is just a number with some value to measure objects or quantities. The resultant of two or more scalar will always be a scalar quantity. Algebraic operations are possible only when two scalar quantities have the same units.
Examples of scalar quantity are – speed, time, mass, electric charge, volume, temperature, gravitational force, etc.
The physical quantity that has both magnitude and direction is called a vector quantity. Because vector quantity has direction, it can be two or threedimensional. Vector algebra is the method to solve vector quantities. It is represented by an arrow over the top of the vector number. The resultant of two vectors can be a scalar or a vector quantity depending upon the algebraic function we have applied.
A dot product of two vectors will result in a scalar quantity, whereas a cross product will result in a vector quantity. Vectors can be resolved into sine and cosine functions to find the direction of the resultant vector. The sine function is used in the dot product of vector quantities, and the cosine function is used in the cross product of the vector quantities.
Examples of vector quantity are – displacement, velocity, electric field, acceleration, polarization, force, linear momentum, etc.


















To reach his home, a boy walks 10 m north, 12 m east, 3 m west, and 5 m south. What is the magnitude of his displacement from his original point?
Answer: We know displacement is a vector quantity because it has both magnitude and direction. The boy also walks in both positive and negative directions if we consider his starting point as origin.
To find the total distance traveled along the yaxis, let us consider the movement towards the north to be positive and the south negative.
∑y = 10m − 5m = 5m
He moved a net of 5 meters to the north along the yaxis.
In the same way, we can consider the boy’s movement towards the east to be positive and the west to be negative.
∑y = −3m + 12m = 9m
He moved a net of 9 m to the east.
Now using Pythagoras theorem, we can find the resultant as
D2 = (∑x2) + (∑y2)
Substituting the values, we get,
D2 = 92 + 52
This gives, D = 10.30m.
Ques: Is force a scalar or vector quantity?
Ans: Force has both magnitude and direction. Hence, it is a vector quantity. Other forces, such as gravitational force, are a scalar quantity as they only have magnitude and no direction.
Ques: Is time a vector quantity of scalar quantity?
Ans: Time is a scalar quantity. It has only magnitude and no direction. Therefore, it never changes its course and moves only in one direction (not a vector direction).