Vector And Scalar Quantities
In mathematics and physics, we have physical quantities which can be categorized in two ways, namely
 Scalar Quantity
 Vector Quantity
In this article, let us discuss what are vector and scalar quantities with examples.
Also, read: 
Scalar Quantity Definition
The physical quantities which have only magnitude are known as scalar quantities. It is fully described by a magnitude or a numerical value. Scalar quantity does not have directions. In other terms, a scalar is a measure of quantity. For example, if I say that the height of a tower is 15 meters, then the height of the tower is a scalar quantity as it needs only the magnitude of height to define itself. Let’s take another example, suppose the time taken to complete a piece of work is 3 hours, then in this case also to describe time just need the magnitude i.e. 3 hours.
Scalar Quantity Examples
Other examples of scalar quantities are mass, speed, distance, time, energy, density, volume, temperature, distance, work and so on.
Vector Quantity Definition
The physical quantities for which both magnitude and direction are defined distinctly are known as vector quantities. For example, a boy is riding a bike with a velocity of 30 km/hr in a northeast direction. Then, as we see for defining the velocity, we need two things, i.e. the magnitude of the velocity and its direction. Therefore, it represents a vector quantity.
Vector Quantity Examples
Other examples of vector quantities are displacement, acceleration, force, momentum, weight, the velocity of light, a gravitational field, current, and so on.
Difference Between Scalar and Vector Quantity
Let us discuss some difference here:
Difference Between Scalar and Vector Quantity 

Scalar Quantity 
Vector Quantity 
It has magnitude only  It has both magnitude and the direction 
It does not have direction  It has direction 
It is specified by a number and a unit  It is also specified by a number along with the direction and unit 
It is represented by quantity symbol  It is represented by quantity symbol in bold or with the arrow sign above 
Example: Temperature, speed, etc  Example: Acceleration, velocity, etc 
Vector Representation
Let us have a look at the line segment drawn below. A vector quantity always has a starting point and an endpoint. The two endpoints of the given line segment are distinguishable as and. It represents a directed line segment
The directed line segment with an initial point A and terminal point B is symbolically denoted as AB in bold or as \(\overrightarrow{AB}\) and the length a of the vector represents its magnitude which is denoted by AB. Instead of using double letter notation we can use a single letter notation to represent a vector as a, b, c and it denotes their magnitudes. As it is difficult to write letters in bold we use a bar above the letters to represent vectors as \(\overline{a}\).
Therefore, if \( \overrightarrow{AB} = a \) then\( \overrightarrow{AB} = a \) where \(\overrightarrow{AB}\) indicates the magnitude of the vector. Also, the magnitude is called the modulus.
Characteristics of Vectors
The characteristics of the vectors are as follows:
 Vectors possess magnitude as well as the direction
 It does not obey the ordinary law of algebra
 Either the magnitude or direction change or both change
Scalar and Vector Quantity Example
Question:
Find out the scalar and vector quantity from the given list.
Force, Speed, Electric field, Angular Momentum, Magnetic Moment, Temperature, Linear Momentum, Average Velocity.
Solution:
From the given list,
 Scalar Quantities – Speed, Temperature.
 Vector Quantities – Force, Electric field, Angular Momentum, Magnetic Moment, Linear Momentum, Average Velocity.
Now we are familiar with what are vectors and scalars. Now if somebody asks if acceleration is a vector or a scalar, we can easily tell that it’s a vector because it has direction as well as magnitude. Similarly, when asked if the distance is a vector or scalar, it is quite evident that as distance has only magnitude, it is a scalar quantity.
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