Scalar and Vector Quantity
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Scalar and Vector Quantity
Sep 26, 2022, 16:45 IST
We usually use the terms force, velocity, speed, and work in physics, classifying these quantities as scalar or vector. A Scalar quantity is that physical quantity with only magnitudes such as mass and electric charge. Whereas a vector quantity is that physical quantity with magnitudes and directions, such as force and mass. In this article, we will learn about scalars and vectors.
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What is Scalar Quantity?
A scalar quantity is that physical quantity with only magnitude and no direction. Such physical quantities can only be described by their numerical value without directions. The addition of these physical quantities follows the simple algebra rules, and here only their magnitudes are added.
Examples of Scalar Quantities
Some examples of scalar Quantities are:
- Mass
- Speed
- Distance
- Time
- Volume
- Density
- Temperature
What is Vector Quantity?
A vector quantity is that physical quantity that has both direction and magnitude.
A vector with a magnitude value equal to one is called a unit vector and is represented by a lowercase alphabet with a "hat" circumflex, i.e., "û."
Examples of Vector Quantities
Some examples of vector quantities are:
- Linear momentum
- Acceleration
- Displacement
- Momentum
- Angular velocity
- Force
- Electric field
- Polarization
Difference between Scalar and Vector Quantity
| Vector | Scalar | |
| Definition | A physical quantity with both the magnitude and direction. | A physical quantity with only magnitude. |
| Representation | A number (magnitude), direction using unit cap or arrow at the top and unit. | A number (magnitude) and unit |
| Symbol | Quantity symbol in bold and an arrow sign above | Quantity symbol |
| Direction | Yes | No |
| Example | Velocity and Acceleration | Mass and Temperature |
Addition and Subtraction Vector
After understanding what a vector is, we will learn how to add and subtract vectors. The addition and subtraction of vector quantities do not follow simple arithmetic rules. A particular set of rules is followed for adding and subtracting vectors. When adding vectors, pay attention to the following points:
- The addition of vectors means finding the result of the number of vectors acting on a body.
- The component vectors whose resultant is to be calculated are independent of each other. Each vector behaves like as if the other vectors were absent.
- Vectors can be added geometrically but not algebraically.
- Vector addition is commutative, i.e.,
Now, subtracting a vector is the same as adding the negative of the vector to be subtracted. For a better understanding, let's look at the example below.
Consider two vectors, A and B, as shown in the figure below. We need to subtract vector B from vector A. This is the same as adding vector B to vector A. The resulting vector is shown in the figure below.
Image
Solved Examples
Q1. Raj walks 10 m north, 12 m east, 3 m west, and 5 m south and then stop to drink water. Find the magnitude of his displacement from his original point.
Ans. As we know that displacement is a vector quantity; hence the direction Raj walks will be positive or negative along an axis.
To calculate the total distance traveled along the y-axis, let us consider the movement towards the north and the south to be positive and negative.
Σy = 10 - 5 = 5m
let's consider his movement towards the east to be positive and the west to be negative.
Σy = -3 + 12 = 9m
Now, using Pythagoras theorem, the resultant displacement can be found as follows:
D 2 = (Σx 2 ) + (Σy 2 )
Substituting the values, we get
D 2 = 92 + 52
D 2 = 1062
√D 2 = √1062
D = 10.30m
Q2. Write the magnitude of a unit vector.
Ans. A unit vector has no dimensions or units. Therefore, Unity is the magnitude of a unit vector.
Frequently Asked Question (FAQs)
Q1. What are two types of physical quantities?
Ans. Physical quantities are classified into two categories:
- Scalar quantities - The physical quantities with a magnitude but no direction are called scalar quantities or scalars.
- Vector quantities - The physical quantities that possess magnitude and direction are called vector quantities or vectors.
Q2. Is temperature a scalar or vector?
Ans . Temperature is a scalar physical quantity; it has a magnitude associated with it but no directional sense. Examples of scalar quantities are pressure, energy, concentration, or density.
Q3. Why is time a scalar quantity?
Ans. Time is a scalar quantity because we usually need only magnitude to describe time.
Q4. Why is the distance a scalar quantity?
Ans . Distance is a scalar quantity because it does not include any direction in its representation.
Q5. Can a scalar be a decimal?
Ans . So far, all the integer scalar values you've seen have been in what usually is called base 10 or decimal notation.
