# Vector and scalar magnitude

The crucial difference between **scalar magnitude and vector magnitude** is that the former is simply associated with the magnitude of any quantity, while the latter is a physical quantity that considers both magnitude and direction. Here in this article we will see some other parameters of differentiation between both concepts, followed by a fabulous and very useful differentiating table.

Index ## Scalar Magnitude | ## Vector Magnitude | |

Associate with | Only magnitude | Magnitude and direction both |

Nature | Simple | Complex |

Representation | Simply by quantity symbol. | Either by quantity symbol in bold or by an arrow over the quantity symbol. |

Variation | The change in quantity is only the result of the change in magnitude. | The change in quantity is the result of the variation in magnitude, direction, or both simultaneously. |

Dimension | Unidimensional | Be it one, two or three dimensional. |

Examples | Distance, temperature, speed, load, frequency, etc. | Displacement, moment, force, electric field, magnetic field, etc. |

## Definition of scalar magnitude

A type of magnitude in which **the measurement is defined only by the magnitude of the measurand** is known as a scalar. In this you never consider the address since your only concern is associated with the amount.

So every time a **change in quantity** is noticed , it is only due to the variation in its magnitude. Basically, scalar quantities follow the basic laws of algebra and can therefore be added, subtracted, multiplied, or divided algebraically, just like normal numbers. However, they must contain the same units.

We know that the basic definition of distance specifies the **total length of a path** that is covered by an object. So distance has nothing to do with direction of movement. Whatever the latter, the length of the route is independent of the direction of movement in case of distance.

It does not matter if the movement is forward-backward or left-right. Only **range of motion** is taken into account . That is why we say that distance is a scalar quantity. The presence of only magnitude makes this quantity simple by nature.

## Definition of vector quantity

A quantity in which the measurement **is defined by both the magnitude and the direction** of the measurand is said to be a vector quantity. So, two quantities of vectors are said to be equal when they have the same magnitude and a similar direction. Therefore, we can say that the change in the number of vectors is associated with the variation in both magnitude and direction. Since direction is associated with quantity, it **does not follow the basic algebraic laws** , despite following the laws of vector algebra.

Vector quantities can never be divided by each other. However, **the vector product** of two quantities can be produced and is said to be the cross product. Let’s take an example of “displacement” of a vector quantity to understand this.

Basically, displacement is defined as the **length of the path covered in a certain direction** by an object. Therefore, we say that in case of displacement, the direction of movement is a crucial factor for its determination. That is why we can say that the magnitude of the displacement can be equal to or less than the full length of the path. Because, if the object moves back and forth, in case of change of direction, the traversed path will be subtracted.

## Key differences between scalar quantity and vector quantity

- A scalar quantity defines the measure only in terms of magnitude. Whereas a vector quantity is associated with a measure in terms of magnitude and direction.
- Scalar quantities have a one-dimensional behavior, while vector quantities can be one, two, or three-dimensional.
- In the case of the scalar quantity, the variation is the result of a change in magnitude only. While in the case of the vector quantity it is the result of magnitude, direction or both.
- Scalar quantities exhibit simplicity in measurement. However, the involvement of the direction along with the magnitude increases the complexity of the vector quantities.
- Generally, to represent a scalar quantity, its magnitude is used together with the unit. While a vector quantity is represented by the magnitude and the unit written in bold or by an arrow over the magnitude.
- Scalar quantities can be easily summarized and subtracted. Also, its product is easily generated and divisible as it follows the basic laws of algebra. But vector quantities follow the laws of vector algebra.
- Examples of scalar quantities are distance, speed, head, pressure, temperature, frequency, time, etc. While quantities like displacement, force, velocity, electric field, magnetic field, and acceleration, etc., are examples of vector quantities