Difference Between Scalar and Vector Quantity

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In the words of Ernest Rutherford, “in science, there is only physics, the rest is just stamp collecting”. In other words, no one can deny that physics is superior to all the branches of science like chemistry, biology, or even mathematics.

However, a well-read person can also not deny that without the involvement of mathematical quantities, physics is too far to be called complete. Such is the case of the scalar and vector quantities. Without the inclusion of these two physical quantities, we can’t define the working of physics.

A scalar only has magnitude and a vector has both magnitude and direction. That’s why scalar quantities are just one-dimensional. And, vector quantities are multi-dimensional.

Difference Between Scalar and Vector Quantities

  Scalar Quantity Vector Quantity

A scalar is a quantity that has magnitude only, but no direction.

A vector is a quantity that has both directions as well as magnitude.
2. It is always one-dimensional, regardless of how they are used. It can be one, two, or three-dimensional, of course, in terms of its use.

Scalar quantity can change in terms of its magnitude only.

Vector quantity can change in terms of either magnitude or its direction of application.
4. For scalars, normal rules of algebra are applicable. For vectors, only vector algebra is applicable.
5. A scalar quantity can completely divide another scalar quantity. A vector quantity can never divide another vector quantity.
6. The resultant of two scalars will always be a scalar quantity. The resultant of two vectors can be either a scalar or a vector quantity.

Examples of scalar quantities are mass, length, time, etc.

Examples of vector quantity are velocity, acceleration, Polarization, etc.


What is a Scalar Quantity?

A scalar quantity is a physical quantity that depends upon its magnitude only. Therefore, it is always one-dimensional. Why? Because it does not have any direction to be a two or three-dimensional quantity.

In other words, scalars are nothing but merely a number accompanied by their measuring units. According to the scalar quantity definition, the resultant of two scalar quantities is always scalar.

Consequently, any algebraic operation is possible, only and only if, both the scalar quantities have the same measuring units. Moreover, a scalar quantity is denoted by nothing. WHY? Because there is no specific direction to represent.

Since the magnitude of a scalar quantity is the same in every direction. Therefore, there is no need to resolve it further.

Must Read: Difference Between Distance and Displacement (Tabular Form)


Examples of Scalar Quantity

There can be so many examples of a scalar quantity. Some of them are listed below!

  • Mass
  • Electric charge
  • Gravitational force
  • Speed
  • Time
  • Charge density
  • volume
  • Temperature, etc.

Must Read: Top 6 Uniform Motion Examples in SIX minutes (All NEW)


What is a Vector Quantity?

A vector quantity is a physical quantity that depends on both magnitudes as well as the direction of its application. Just because a vector quantity has direction, it can be either one, two, or three-dimensional quantity.

According to the vector quantity definition, a vector can only be solved using vector algebra. A vector quantity is denoted by an arrow placed over the magnitude of the vector.

Moreover, the resultant of two vector quantities can either be a scalar or a vector, of course, depending on the method of its application.

In other words, the dot product of two vectors is a scalar quantity. That’s why the dot product of vectors is also known as the scalar product.

Similarly, the cross-product of two vectors is a vector quantity. That’s why the cross-product of vectors is also known as the vector product. Furthermore, the vectors can be resolved with the help of the sine or cosine of the angles between two vector quantities.

To put it differently, the dot product of vectors is resolved with the help of the sine of the adjacent angles. On the other hand, the cross-product of vectors is resolved with the help of the cosine of the adjacent angles.


Examples of Vector Quantity

There can be so many vector quantity examples in real life. Some of them are listed below!

  • Velocity
  • Acceleration
  • Electric field
  • Displacement
  • Polarization
  • Linear momentum
  • Force, etc.


Frequently Asked Questions

1. Is force a vector or scalar?

Ans. In spite of the fact that a force has both magnitude and direction. However, for some kinds of forces (gravitational force), their magnitude can be defined as being a scalar quantity.

In other words, the gravitational force acting on a particle is definitely not a scalar, but its magnitude is.

2. Is time a vector?

Ans. Well, to date, there is no formal definition of time. But, as per the scientific community, time is definitely not a vector quantity, in fact, it’s a scalar one. Why? Because its direction never changes, it always moves in the forward direction

3. Is temperature a scalar or a vector quantity?

Ans. Well, it’s a tricky question. I mean, the temperature can be either scalar or a vector quantity, of course, depending on the way of its measurement.

For example, if you are measuring a constant temperature, then it’s a scalar quantity. Conversely, the measurement of the decrease or increase of the temperature is a vector quantity.

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I am currently working with Cuemath as an online maths educator and teaching students from all over the world. Since I did my BSc in non-medical where I chose physics in my master's (MSc) and decided to deliver my knowledge to help the students in grasping the respective topics of physical sciences by having a glance at my articles.

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