Scalar and vector quantities used to be a thorough subject of debate among physicists for many years. It took a lot of studies and papers for a clear difference between the two quantities to emerge. These days it is quite easy to make a distinction between a scalar and a vector quantity.

## Scalar Quantity

**Scalar quantity **is
defined by only one element referred to as **magnitude**,
without which there is no scalar quantity. Therefore, a scalar is usually said to be a
physical quantity that only has magnitude and no other characteristics. **Magnitude** means the size of the
quantity such as length or strength.

A scalar is any number that gives the size or magnitude of a quantity, therefore a unit of measurement must be attached to the number like degrees or meters. Any random number is not a scalar. For example number 25 is meaningless unless you tell us that 25 is a measurement of something like distance or time or temperature.

### What You Need To know About Scalar Quantity

- Scalar quantity implies that the physical quantity has only magnitude and no direction.
- Any change in scalar quantity indicates only change in magnitude of the concerned physical quantity.
- Scalar quantities are always one dimensional.
- The scalar quantity can divide another scalar quantity.
- Scalar quantity follows ordinary rules of algebra. Therefore, normal algebraic method can be used to solve scalar quantity.
- Any mathematical calculation/operation between two or more scalar quantities will always result to a scalar quantity.
- Any mathematical operation between a scalar quantity and a vector quantity will always result to a vector quantity.
- Scalar quantity cannot be resolved; it has exactly same value in all directions.

### Examples of Scalar Quantities

- Speed
- Work
- Distance
- Power
- Temperature
- Volume
- Charge
- Gravitational potential
- Frequency
- Energy
- Length
- Kinetic energy
- Specific heat
- Power
- Calorie
- Density
- Entropy

## Vector Quantity

**A vector quantity**can be defined by two elements, **magnitude
and direction.** Without these two elements a physical quantity cannot be
defined as a vector. Therefore, a vector quantity can be defined as a physical
quantity that comprises of **both
magnitude and direction.** **Magnitude**means the size of the quantity such as length or strength. **Direction** means the position where the vector is pointing to or
where it is being directed such as left or right, east, west, north or south
(up or down).

When a vector is drawn, it is represented by an arrow whose length represents the vector’s magnitude and whose arrow head points in the direction of the vector.

### What You Need To know About vector Quantity

- Vector quantity implies that the physical quantity comprise of both magnitude and direction.
- Any change in vector quantity indicates changes either in magnitude or in direction or in both.
- Vector quantities can be either one or two or three dimensional.
- Two vectors cannot be divided or can never divide.
- Vector rules follows rules of any mathematical operation. Geometry method can be used to solve vector quantity.
- Mathematical operation between two or more vector quantities may give either vector or scalar quantity.
- Mathematical operation between vector and scalar quantities will result to a vector quantity.
- Vector quantity can be resolved in two mutually perpendicular directions using the adjacent angle.

### Examples Of Vector Quantities

- Force
- Acceleration
- weight
- Shearing Stress
- velocity
- Electric field intensity
- Centrifugal force
- Torque
- Momentum
- Electric flux

### Quantities That Are Both Vector And Scalar

- Mass
- Weight
- Speed
- Work
- Power
- Energy
- Displacement
- Distance
- Force
- Torque

**Also Read: ***Difference Between Mass And Weight*

## Difference Between Scalar And Vector Quantity In Tabular Form

BASIS OF COMPARISON | SCALAR QUANTITY | VECTOR QUANTITY |

Description | Scalar quantity implies that the physical quantity has only magnitude and no direction. | Vector quantity implies that the physical quantity comprise of both magnitude and direction. |

Change | Any change in scalar quantity indicates only change in magnitude of the concerned physical quantity. | Any change in vector quantity indicates changes either in magnitude or in direction or in both. |

Dimensional | Scalar quantities are always one dimensional. | Vector quantities can be either one or two or three dimensional. |

Division Of Quantity | The scalar quantity can divide another scalar quantity. | Two vectors cannot be divided or can never divide. |

Mathematical Rules | Scalar quantity follows ordinary rules of algebra. | Vector rules follows rules of any mathematical operation. |

Mathematical Operation Between Two or More Quantities | Any mathematical calculation/operation between two or more scalar quantities will always result to a scalar quantity. | Mathematical operation between two or more vector quantities may give either vector or scalar quantity. |

Mathematical Operation Between A Scalar Quantity And A Vector Quantity | Any mathematical operation between a scalar quantity and a vector quantity will always result to a vector quantity. | Mathematical operation between vector and scalar quantities will result to a vector quantity. |

Direction | Cannot be resolved; it has exactly same value in all directions. | Can be resolved in two mutually perpendicular directions using the adjacent angle. |

## What Are Some Of The Similarities Between Scalar Quantity And Vector Quantity

- Both have some specific unit and dimension.
- Both scalar and vector have magnitude.
- Both scalar and vector quantity are measurable.
- Both can express certain physical quantity.
- Mathematical operation between vector and scalar quantities will result to a vector quantity.

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