**What are Scalar and Vector quantity?**

When we think about **Scalar and vector** the first thing comes into our mind is Science because the term scalar and vector are specified and explained in Science only. After science, the second thing that comes to our mind is about quantity because we name scalar and vector as quantities like scalar quantity and vector quantity. We think that there is nothing to say about scalar and vector as they are only quantities and as it comes under science (Physics) Part.

**Difference between Scalar and Vector**

**Scalar** – A scalar is a quantity that is fully described by a magnitude only. It is described by just a single number. Some examples of scalar quantities include speed, volume, mass, and time.

**Vector** – A vector is a quantity that has both a magnitude and a direction. Vector quantities are important in the study of motion. Some examples of vector quantities include force, velocity, acceleration, and momentum.

**Scalar Quantities** : The physical quantities which are specified with the magnitude or size alone are Scalar quantities. For example, length, speed__, __work, mass, density, etc.

**Vector Quantities** : Vector quantities refer to the physical quantities characterized by the presence of both magnitude as well as direction. For example, displacement, force, torque, momentum, acceleration, velocity, etc.

The term ‘scalar quantity’ is defined as a quantity that has only one element of a number field, attached to a unit of measurements, such as degrees or meters. It is a quantity that exhibits magnitude or size only, i.e. it is defined by a numerical value, along with a measurement unit. For example, Speed of the car, body temperature, distance between two locations, etc.

The term vector quantity is defined as A mathematical quantity that needs two independent characteristics to describe it completely, i.e. magnitude and direction. Here magnitude represents the size of the quantity which is also its absolute value, while direction represents the side, i.e. east, west, north, south, etc. For example, Displacement between two points, velocity, and acceleration of a moving body, force, weight, etc..The uses of scalar quantity are: In physics, two scalar quantities that you’ll work with often are **mass** and **charge**. The mass of an object measures how much matter the object is made of.

When you step on a scale that uses a balancing arm, the result you get is your mass. The charge of an object is how much voltage it is emitting. The uses of vector quantity are : **Vectors** can be used to represent physical **quantities**. Most commonly in physics,** vectors** are used to represent displacement, velocity, and acceleration. The length represents the magnitude and the direction of that **quantity** is the direction in which the** vector** is pointing. Then we just start thinking that what are general vectors and their notations…So here we are, **Vector notation** is a commonly used mathematical notation for working with mathematical vectors, which may be geometric vectors or members of vector spaces. To denote vectors, arrows are marked above the representative symbols for them.

Examples include AB→, BC→ , and so on. Single letters also would be suitable for this purpose like:

*Velocity vector: V*

*Force vector: F*

*Linear momentum: p*

*Acceleration** vector: a*

* *

After this, we can also think about,

**How vectors are represented: **

*One could represent this using a parallel line drawing on velocity and to show the direction, mark an arrow for the same.*

*The difference between scalar quantity and vector quantity is as follows: – *

BASIS FOR COMPARISON |
SCALAR QUANTITY |
VECTOR QUANTITY |

Meaning |
Any physical quantity that does not include direction is known as a scalar quantity. |
A vector quantity is one, that has both magnitude and direction. |

Quantities |
One-dimensional quantities |
Multi-dimensional quantities |

Change |
It changes with the change in their magnitude. |
It changes with the change in their direction or magnitude or both. |

Operations |
Follow ordinary rules of algebra. |
Follow the rules of vector algebra. |

Comparison of two quantities |
Simple |
Complex |

Division |
Scalar can divide another scalar. |
Two vectors can never divide. |

What does scalar quantity follow…??

The rules of ordinary algebra can be applied for combining scalar quantities, such that scalars can be added, subtracted or multiplied, in the same way, as numbers. However, the operation of the scalar can only be possible, for the quantities with the same measurement unit.

What does the vector quantity follow…??

A vector quantity follows the triangle law of addition. An arrow is used to indicate vector quantity, placed over or next to the symbol that denotes vector.

**The summary of scalars and vectors is as follows:** In* short, scalar quantity gives you an idea about how much of an object there is, but vector quantity gives you an indication of how much of an object there is and that also in which direction. So, the main difference between these two quantities is associated with the direction, i.e. scalars do not have direction but vectors do.*

Read another topic on **Motion in a Straight Line**

*Questions for Exams:*

*1. What are the differences between scalars and vectors?*

*2. What is the real-life application of scalar and vector?*

*3. Introduction to scalars and vectors.*

*4. Definitions and examples + uses of scalar and vector quantities?*

* Scalar and Vector quantities*

A scalar quantity has only magnitude.

A vector quantity has both magnitude and direction.

Scalar Quantities |
Vector Quantities |

Length, area, volume | Displacement |

Speed | Velocity |

Mass, density | Acceleration |

Pressure | Momentum |

Temperature | 4 Force |

Energy, entropy | Lift, drag, thrust |

Work, Power | Weight |

*5. What do scalar and vector quantities follow?*

*6. What is the use of these two quantities (scalar and vector) In day to day life?*

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