Mathematics is the language of Physics. With this, we can describe the world around us in quantitative terms. For mechanics (energy, mass, and time), we can utilize two types of amounts to numerically depict ideas. 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.

**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. Its the quantity which you can write down numerically.

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

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 Between Scalar and Vector (in Tabular Form)

Parámetro de comparación | Scalar | Vector |
---|---|---|

Definición | Scalar has only magnitude but there is no direction | Vector has both magnitude and direction |

Problem | With 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 |

Change | We can make changes in scalar quantity by changing its magnitude | Vector quantities can be changed with a change in magnitude and direction. |

Naturaleza | Simple rules of addition, subtraction, multiplication, and division can be used here. Scalar quality can divide another scalar quality | For Vector quantities, we cannot operate addition, subtraction, multiplication, and division by using arithmetic rules. Therefore one vector can’t divide another vector |

Ejemplos | Time, speed, mass, Area, Density, Work, etc | Displacement, 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 completely 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.

Preparing food in our kitchen or to grow crops in our farm, temperature plays a very important role and it’s a scalar quantity because it has only magnitude.

## What is Vector?

Now we understand the definition of Vector that is the physical quantity with a magnitude as well as direction. It is represented by an arrow 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 it 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 Law, Second Law, and Third law are not even possible to understand without the use of Vector.

In sports like basketball, Cricket, 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 if we are making even a small change in either its magnitude or direction, a vector can be changed. Hence, if we rotate a ball at some angle, it’s 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 Vector multidimensional problems can be solved by using this.

**Main Differences Between Scalar and Vector**

- Scalar are those physical quantities that have only magnitude but no direction, and Vectors are those physical quantities that have both magnitudes as well as direction.
- One dimensional problem can be solved with the help of the Scalar whereas with the help of Vectors, multidimensional problems can be solved.
- 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.
- Scalar quantity can divide another Scalar quantity. But in the case of Vector, it’s not that simple because one vector entity can’t divide another vector entity.
- Example of scalar quantities – speed, work, distance, energy, power, temperature, volume, specific heat, density, entropy, gravitational potential, frequency, kinetic energy, etcetera.
- Examples of vector quantities: velocity, torque, momentum, magnetic field intensity, force, acceleration, etcetera.

## Conclusión

It is very important to understand the basics for the Scalar and Vector and also how these quantities are used in our day to day life.

Books for undergraduates give a short description of the nature of Scalar and Vector Quantities, and for many students, the short description can create lots of confusion.

Now we have been able to differentiate between Scalar and Vector quantities, but also we have to keep in mind that quantities can have both magnitude and direction which are not considered as a Vector.

For example, electric current and pressure are some physical quantities that have magnitude and direction but still are not considered as Vectors because these quantities do not follow the laws of vector addition. In this way, the electric flow is a scalar amount.

## Referencias

- https://iopscience.iop.org/article/10.1088/1475-7516/2006/03/004/meta
- https://ieeexplore.ieee.org/abstract/document/398877/
- https://ieeexplore.ieee.org/abstract/document/250686/
- https://aip.scitation.org/doi/abs/10.1063/1.2829861

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