The physical quantities that are used in Physics which includes velocity, acceleration, speed, etc. these physical quantities are categorized as either scalar or vector quantities. So on what basis do we classify these physical quantities as scalar and vector? The answer to this question is by defining these terms.

What is a scalar?

A scalar quantity is defined as the quantity that has only magnitude. The examples of scalar quantities are mass, electric charge, etc that has only magnitude, that is, these quantities have only values.

What is a vector?

A vector quantity is defined as the quantity that has both magnitudes as well as direction. The examples of vector quantities are weight, acceleration, etc that has both value and direction.

What is the vector notation?

Vectors are differentiated from the scalar quantities with the help of notation. The most commonly used vector notations are either the bold letters are used or arrow mark is used on top of the letter to represent that the quantity is a vector.

An example of vector notation is a force is either F or

What is the difference between a scalar and a vector?

Following is a table explaining the difference between a scalar and a vector:

Scalar  Vector 
It has just magnitude It has both magnitudes as well as the direction
It is used for one-dimensional quantities It is used for multidimensional quantities
For the calculation of scalar quantities, normal algebra are used For the calculation of vector quantities, vector algebra are used
Speed and time are examples of scalar quantities Velocity and force are examples of vector quantities


Facts about scalars and vectors

Following are a few interesting facts about scalars and vectors:

  • Unit vectors are used for defining the direction and their magnitude is equal to 1.
  • Irish physicist William Rowan Hamilton invented the vector quantities.
  • Scalars and vectors quantities find applications in Mathematics and Science.
  • Vectors are used for defining multidimensional spaces.
  • Vector graphics are used in computers as they don’t lose their image quality irrespective of the size they are scaled to.

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