Scalars And Vectors

Any physical quantity can be grouped into two categories; Scalar and Vector. A physical quantity with only magnitude is called scalar quantity. A physical quantity with magnitude and direction is called vector quantity. Represented by an arrow at the top. Scalar and vector example is, velocity is a vector quantity. It’s scalar equivalent is speed.

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

Scalars Quantity

Some physical quantities can be described just by their numerical value (with their respective units) without directions (they don’t have any direction). In general, Any physical quantity with magnitude and no direction is called scalar. The addition of these physical quantities follows the simple rules of the algebra. That is only their magnitudes are added.

Scalars Quantity Examples

There are plenty of Scalars Quantity examples, Some of them are Mass, Speed, Distance, Time, Area, Volume, Density, Temperature, Energy, Power, etc.

Scalar Addition

To illustrate scalar addition let us consider Mass, The unit of mass is kg. Adding two masses say; 5kg and 7kg, gives the resultant mass of (5 + 7) kg = 12kg.

Scalar and Vector

What Is Vector Quantity

Sometimes, to describe certain physical quantity, Direction plays a major role along with magnitude. Thus, to answer to what is Vector Quantity? is Any physical quantity that has both direction and magnitude is called vector quantity. A vector with the value of magnitude equal to one and direction is called unit vector represented by a lowercase alphabet with a “hat” circumflex. That is “û“.

Vector Addition

The addition of vector quantities does not follow the simple arithmetic addition. To add vector quantities, a special set of rules are followed for the addition and subtraction of vectors.

Vector Quantities Examples

Vector quantity examples are many. Some of them are, Force, Displacement, Linear momentum, Weight, Acceleration, momentum. To explain clearly, let us consider an example of vector quantity that is;
Velocity is a vector quantity since it has both magnitude (numerical value) and direction. If you are saying that the velocity of a certain object is 5 m/s, it is incomplete since the direction of velocity is not mentioned. Velocity could be in any direction, so a certain direction has to be assigned to it in order to give complete information.

Following is the table explaining other scalar and vector related concepts:

Difference Between Scalar and Vector

The difference between Scalar and Vector is crucial to understand in physics learning. Below is the list of differences for better understanding.

  • Scalars are physical quantities which can be completely described by their numerical value.
  • Vectors are physical quantities which require both magnitude and direction for a complete description.


Scalar And Vector Quantities Problems With Solutions

Q1: What is a scalar quantity?

Answer: A scalar is a one-dimensional quantity of measurement with magnitude only.

Q2: Give a few examples of scalar quantities.

Answer: A few examples of scalar quantities are:

  • Distance
  • Temperature
  • Mass
  • Speed

Q3: What is vector quantity?

Answer: A vector quantity is a physical quantity which has magnitude as well as direction.

Q4: Write vector quantity examples.

Answer: A few vector quantity examples are:

  • Acceleration
  • Force
  • Velocity
  • Momentum
  • Energy
  • Work

Q5: Write a few differences between scalar and vector quantities.

Answer: A few differences between scalar and vector quantities are as follows:

Scalar Quantity Vector Quantity
A scalar quantity has only magnitude A vector quantity has both magnitude and direction
Normal rules of algebra are applicable A different set of rules known as the vector algebra is applicable
A mathematical operation between two or more scalar quantities will always fetch a scalar quantity A mathematical operation between two or more vector quantities may either fetch a vector or a scalar quantity
Scalar quantities are one dimensional Vector quantities are either one, two or three dimensional

Q6: Given below is a list of quantities. Categorize each quantity as being either a vector or a scalar.

20 degrees Celsius
5 mi., North
256 bytes
5 m
30 m/sec, East
4000 Calories

Answer:

20 degrees Celsius Scalar
5 mi., North Vector
256 bytes Scalar
5 m Scalar
30 m/sec, East Vector
4000 Calories Scalar

Q7: Ashwin walks 10 m north, 12 m east, 3 m west and 5 m south and then stops to drink water. What is the magnitude of his displacement from his original point?

Answer: We know that displacement is a vector quantity, hence the direction Ashwin walks will either be positive or negative along an axis.

Now, to find the total distance traveled along the y-axis, let us consider the movement towards the north to be positive and the movement towards the south to be negative.

\(\sum y=10\,m-5\,m=5\,m\)

He moved a net of 5 meters to the north along the y-axis.

Similarly, let us consider his movement towards the east to be positive and the movement towards the west to be negative.

\(\sum y=-3\,m+12\,m=9\,m\)

He moved a net of 9 m to the east.

Using Pythagoras theorem, the resultant displacement can be found as follows:

\(D^2=(\sum x^2)+(\sum y^2)\)

Substituting the values, we get

\(D^2=(9^2)+(5^2)\) \(D^2=(106)^2\) \(\sqrt{D^2}=\sqrt{(106)^2}\) \(D=10.30\,m\)

This was just an introduction to scalar quantities and vectors quantities. To learn in details about Scalar And Vector, download BYJU’S – The Learning App.


Practise This Question

Find component of vector A along the direction of B i.e. A||B and in perpendicular direction of B that is AB.