Scalars and Vectors: Understanding the Key Differences

Scalars and Vectors: Understanding the Key Differences

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Vikram
Vikram Singh
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Updated on Aug 29, 2023 14:01 IST

Physical quantity with magnitude and no direction is known as a scalar quantity and a physical quantity with magnitude and directions is known as a vector quantity. In this article, we will learn the differences between scalar and vector quantity.

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Table of Content

Scalar vs. Vector: Difference Between Scalar and Vector Quantity

Parameter Scalar Quantity Vector Quantity
Definition Physical quantity with magnitude and no direction. Physical quantity with magnitude and directions.
Dimensional One-Dimensional Two or Three-Dimensional
Resultant Resultant of two scalars is a scalar.  Resultant of two vectors may or may be vectors depending upon the algebraic operations performed.
Representation Number and a unit Arrow at the top and a unit
Example Length, Mass, Temperature Displacement, Velocity, Force
Types of Matrix Transpose of Matrix
Symmetric Matrix Skew-Symmetric Matrix

What is a Scalar Quantity

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

Example: Length, Mass, Temperature, Area, Gravitational Force etc.

Scalar quantities can be added, subtracted, or multiplied using the ordinary algebraic operation, but the operation can be performed only on the scalar quantities that have same units.

The following are the properties of scalar quantity:

  1. Scalars have magnitude only, and no direction.
  2. The arithmetic operations of addition, subtraction, multiplication and division can be performed on scalars.
  3. Scalars are independent of direction, so they can be represented by a single value.
  4. Scalars are not affected by rotation or translation.
  5. Scalars can be measured using units of measurement such as meters, joules, or degrees Celsius.
  6. Scalars can be represented by real numbers.
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What is a Vector Quantity

A vector quantity is a physical quantity that has both magnitude and direction.

Examples of vector quantities include velocity, force, and acceleration.

Vector quantity can be added using triangle law of parallelogram and are multiplied using dot product and cross product.

The following are the properties of vector quantity:

  1. Vectors have both magnitude and direction.
  2. The arithmetic operations of addition and subtraction can be performed on vectors.
  3. Vectors can be represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.
  4. Vectors are affected by rotation and translation.
  5. Vectors can be measured using units of measurement such as meters per second or newtons.
  6. Vectors can be represented by mathematical objects such as coordinates or unit vectors.
  7. Vectors can be represented graphically using vector diagrams.
  8. Vectors can be broken down into their components in different directions.
  9. Two vectors are equal if they have the same magnitude and direction.
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Key Similarities and Differences Between Scalar and Vector Quantities

  • Both scalar and vector quantities represent a physical quantity.
  • Both Scalar and Vector quantities are measurable.
  • Vector quantities have both magnitude and direction, while scalar quantities only have magnitude.
  • The resultant of scalar quantity always be a scalar (i.e., real number), while the resultant of vector quantity may or may not be a vector depending upon the algebraic operation performed.
  • A scalar quantity can be divided further into a scalar quantity, but a vector quantity can’t be divided further.
  • Scalar quantities describe only one-dimensional quantities, but multi-dimensional quantities are described using vectors.

Conclusion

In this article, we have learned:

  • Difference Between Scalar and Vector Quantity
  • Properties of Scalar Quantity
  • Properties of Vector Quantity

Hope you will like the article.

Also Read: Matrix Multiplication

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FAQs

What is a Scalar Quantity?

A scalar quantity is a physical quantity that has only magnitude, and no direction. Example: Length, Mass, Temperature, Area, Gravitational Force etc.

What is a Vector Quantity?

A vector quantity is a physical quantity that has both magnitude and direction. Examples of vector quantities include velocity, force, and acceleration.

What is the difference between scalar and vector quantity?

Vector quantities have both magnitude and direction, while scalar quantities only have magnitude. The resultant of scalar quantity always be a scalar (i.e., real number), while the resultant of vector quantity may or may not be a vector depending upon the algebraic operation performed.

About the Author
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Vikram Singh
Assistant Manager - Content

Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio

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