We invented mathematics and science in order to understand and describe the world surrounding us. As a result, we use many mathematical quantities in Physics for explaining the concepts in a clear manner. Thus, a few examples of these are force, speed, velocity and work. Moreover, we often describe these quantities as a scalar or a vector quantity. Further, we differentiate scalars and vectors depending on their definition. Therefore, let us discuss scalars and vectors in detail over here.

**Table of content**

**Introduction to ****Scalars And Vectors**

We define a scalar quantity as the physical quantity that has only magnitude, for instance, mass and electric charge. On the other hand, we define a vector quantity as the physical quantity that has both magnitude and direction like force and weight. Further, we can also differentiate these two quantities by using a notation.

**Definition of Scalar Quantity**

We define scalar quantity as the physical quantity having magnitude and no direction. Moreover, we can describe physical quantities merely by their numerical value, with their respective units, without directions.

In addition, the addition of these physical quantities follows the simple rules of the algebra. So, you see that we only add their magnitudes.

**Examples of Scalar Quantities**

There are a lot of scalar quantity examples, some of the most common examples include:

- Mass
- Speed
- Distance
- Time
- Area
- Volume
- Density
- Temperature

**Definition of Vector Quantity**

We define a vector quantity as the physical quantity which has both directions in addition to magnitude. A vector with the value of magnitude equal to one and direction is referred to as the unit vector. We represent it by a lowercase alphabet with a “hat” circumflex. That is “**û**“.

**Examples of Vector Quantities**

There are many examples of a vector quantity, some of them are as follows:

- Linear momentum
- Acceleration
- Displacement
- Momentum
- Angular velocity
- Force
- Electric field
- Polarization

**Difference Between Scalars and Vectors**

In order to understand it better, we will look at the difference between scalars and vectors.

Basis of Comparison |
Vector |
Scalar |

Definition |
A physical quantity with both magnitude and direction. | A physical quantity with only magnitude. |

Direction |
Yes | No |

Example |
Velocity and Acceleration | Mass and Temperature |

Representation |
A number (magnitude), direction using unit cap or arrow at the top and unit. | A number (magnitude) and Unit |

Symbol |
Quantity symbol in bold and an arrow sign above | Quantity symbol |

**Is it a scalar or a vector?**

- When the football player runs 10 miles an hour towards the end zone.

It is vector as it represents a magnitude (10 mph) and a direction (towards the end zone). This vector represents the velocity of the football player.

- The volume of that box at the west side of the building is 12 cubic feet.

This is a scalar. It can seem to be a bit tricky as it tells us the location of the box at the west side of the building, however, this has nothing to do with the direction of the volume which has a magnitude of 12 cubic feet.

- The temperature of the room was 15 degrees Celsius.

It is a scalar as there isn’t any direction.

- The car accelerated north at a rate of 3 meters per second squared.

This is a vector as it has both direction and magnitude. We also know that acceleration is a vector quantity.

**More about Scalars and Vectors **

- Unit vectors are vectors with a magnitude of 1. We use them to define direction.
- The credit for the invention of vectors is generally given to Irish physicist William Rowan Hamilton.
- Vectors and scalars are essential in various fields of math and science.
- We can define vectors in two dimensional or three-dimensional space.
- We sometimes use vector graphics in computers as we can scale them to a larger size without losing any image quality.

**FAQ on ****Scalars And Vectors**

**Question 1: ****What is a Vector Quantity?**

**Answer 1: **We define a vector quantity as the physical quantity which has both directions in addition to magnitude. A vector with the value of magnitude equal to one and direction is referred to as a unit vector. We represent it by a lowercase alphabet with a “hat” circumflex. That is “**û**“.

**Question 2: Give some examples of a scalar quantity.**

**Answer 2: **There are a lot of scalar quantity examples, some of them are Mass, Speed, Distance, Time and Area.