Let us discuss today about two quantities called scalars and vectors. Suppose you are going in your car or bike. Your vehicle must have speedometer which shows the speed. Let the speed is 60 km/hour. Now suppose you have certain instrument which shows that you are going in north direction with 60 km/hour.
So the 60 km/hr means only the magnitude or value. So the quantities which have only magnitudes or values are called scalars.
But the 60 km/hr in north direction means the quantity has value as well as direction in it. These quantities are called vector quantities.
Therefore the more technical definitions will be:
Scalar quantity: A scalar quantity has magnitude only. Thus mass, length, volume, electric potential and energy are scalars.
Vector quantity: A vector quantity has both magnitude and direction.
For example force, velocity, the electric field intensity and displacement
are examples of vectors.
Graphically, the vector A is represented by a line whose length is equal to the magnitude of A, denoted by |A| and with an arrowhead at the end of the line pointing towards
the direction of A.
Equality of Vectors: Two vectors A and B are equal if and only if their magnitude as well as directions is the same.
Addition and Subtraction of Vectors: Two vectors are added by using parallelogram law. Two vectors represented by the sides of a parallelogram, the sum represents the bigger diagonal.
Addition of two vectors:
Vector addition is commutative that is A + B = B + A.
Subtraction of vectors:
A – B = A + (-B)
A – B is also diagonal of the parallelogram between the tip of A to the tip of B.
Multiplication of a vector by a scalar: Multiplication of a vector by a scalar changes the magnitude of the vector but the direction remains the same. A vector A multiplied by a scalar K will become KA.
Reference: This article is referred from my authored book “concepts of electromagnetic field theory” having ISBN 978-81-272-5245-8. In case of any doubt in this article or any other EMFT or physics related article, kindly post in the comment section.