Difference Between Scalar and Vector

Mathematics is the language of Physics. With this, we can describe the world around us in quantitative terms.


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For mechanics (energy, mass, and time), we can utilize two types of amounts to depict ideas numerically. The two forms are known as vectors and scalars.

Every physical quantity in the world of physics is either Scalar or Vector. Scalar and vector quantities are used in both physics as well as mathematics.

Key Takeaways

  1. Scalar quantities are values with only magnitudes, such as distance, speed, or temperature, and do not have a specific direction.
  2. Vector quantities are values with both magnitude and direction, such as displacement, velocity, or force, and are often represented graphically using arrows.
  3. The main difference between scalar and vector quantities is the inclusion of direction in vector quantities, which adds complexity and requires additional mathematical techniques for manipulation and analysis.

Scalar vs Vector

When we are dealing with physics, there are different types of measurement tools. Scalar and vector are one of those measurement tools.

Scalar or Scalar quantities are those which have only magnitude. Now to understand this Scalar quantity. First, you have to understand the term magnitude.

Magnitude refers to the size of any object, speed of the object or weight of an object. It’s the quantity which you can write down numerically.

A vector is a measuring tool for quantities that have both magnitudes as well as directions, and when a quantity has both magnitude and direction, then we can say that it is a vector quantity.

Scalar vs Vector

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Vector was not developed in its current form until the late 19th century. Irish physicist William Rowan Hamilton”  was the one who handled inventing the concept of Vector.


Comparison Table

Parameter of ComparisonScalarVector
DefinitionScalar has only magnitude, but there is no directionVector has both magnitude and direction
ProblemWith the help of these, only problems of one dimension can be solved. When it comes to multidimensional problems it’s not useful.Multi-dimensional problems can be solved with the use of this tool
ChangeWe can make changes in scalar quantity by changing its magnitudeVector quantities can be changed with a change in magnitude and direction.
NatureSimple addition, subtraction, multiplication, and division rules can be used here. Scalar quality can divide into another scalar quality.We cannot operate addition, subtraction, multiplication, and division for Vector quantities by using arithmetic rules. Therefore one vector can’t divide another vector.
ExamplesTime, speed, mass, Area, Density, Work, etcDisplacement, Force, Velocity, Acceleration, Momentum, etc


What is Scalar?

In material science, a scalar or scalar amount is a physical amount. It does not have any dependence on the direction.

Scalar is utilized to portray one-dimensional amounts.

A physical quantity entirely defined by its magnitude; examples of scalars include distance, density, velocity, energy, mass, and time is called a scalar quantity.

The most used scalar quantities in our daily life are temperature and speed.

In preparing food in our kitchen or growing crops on our farm, temperature plays a vital role, and it’s a scalar quantity because it has only magnitude.

scalar quantity

What is Vector?

Now we understand the definition of Vector, which is the physical quantity with a magnitude as well as direction. An arrow represents it, and the direction of this arrow is the same as that of the quantity.

A vector is known as a unit vector when its magnitude is 1, and this unit vector is used to define the direction.

A vector has direction and magnitude but doesn’t have a position. For calculating every vectorial unit, we need a vector, so we need to understand this term.

Vector is being used in our day-to-day life to locate objects and individuals. Newton’s First, Second, and Third laws are impossible to understand without using Vectors.

In sports like basketball, Cricket, and Baseball, Vector is used by the players. The player throws the ball or shoots the target with an angle in a direction.

Vector has military usage in projectiles/trajectory and even while designing a roller coaster.

If a vector is rotated through an angle, it’ll change.

A vector is defined because of its magnitude and direction. So a vector can be changed if we are making even a small change in either its magnitude or direction.

Hence, if we rotate a ball at some angle, its direction will change, and we can say that the vector has changed.

We can define a vector in two-dimensional and three-dimensional space. Due to this characteristic of Vectors, multidimensional problems can be solved by using this.

vector quantity

Main Differences Between Scalar and Vector

  1. Scalar is those physical quantities that have only magnitude but no direction, and Vectors are those physical quantities that have both magnitudes as well as direction.
  2. The one-dimensional problem can be solved with the help of the Scalar, whereas with the help of Vectors, multidimensional problems can be solved.
  3. By using simple arithmetic rules, Scalar Quantities can be added, subtracted, multiplied and divided, but Vector quantities do not use algebraic rules and need different operations to add, subtract or multiply.
  4. Scalar quantity can divide into another Scalar quantity. But in the case of Vector, it’s not that simple because one vector entity can’t divide another vector entity.
  5. Examples of scalar quantities – are speed, work, distance, energy, power, temperature, volume, specific heat, density, entropy, gravitational potential, frequency, kinetic energy, etcetera.
  6. Examples of vector quantities: are velocity, torque, momentum, magnetic field intensity, force, acceleration, etcetera.
Difference Between X and Y 41
  1. https://iopscience.iop.org/article/10.1088/1475-7516/2006/03/004/meta
  2. https://ieeexplore.ieee.org/abstract/document/398877/
  3. https://ieeexplore.ieee.org/abstract/document/250686/
  4. https://aip.scitation.org/doi/abs/10.1063/1.2829861
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