Earlier in other articles, I have talked about what are Physical Quantities in Science. Let me shortly explain again here and then we will be moving into discussing Scalar and Vector quantities.

So anything which can be measurement by some instrument is called a Physical Quantity. And it is made up of two things **number** and a **unit**. For example – length of my working desk table is 10 metre. Here 10 is a number and metre is unit which is being used to measure length.

Moreover in other articles, I have already discussed about different types of units which can be used for measuring Physical Quantities. Also some Physical Quantities measurement can be too large or very small like 100000000 or 0.00000001

In order to express these measurements of Physical Quantities, we can use **Scientific Notation** according to which

100000000 can be written as 10^{8}

0.00000001 can be written as 10^{-8}

But one important piece which is missing here is **direction**, so saying length is 10 metre does not indicate any direction in which length actually is?

But saying that I applied 10 N force on a box in east – does have a direction.

So based upon whether a Physical Quantity have a direction or not. We have two types of quantities – Scalar or Vector.

Table of Contents

## Scalar Quantities

A Physical Quantity which has just magnitude only but no direction is called a Scalar Quantity or a Scalar.

Symbol for denoting Scalar Quantities are usually written

Like

m for mass

l for length

s for speed

Examples of Scalar Quantities are mass, length, energy, temperature, speed etc. All these quantities just have magnitude and a unit, but no direction.

Like mass of a ball is 0.1 kg or temperature of my room is 30 **°**C. Both of these don’t have a direction.

Moreover Scalar Quantities can be added, subtracted, multiplied or divided with each other just by using simple ordinary laws of algebra.

So we put a box of weight 10 kg into a truck which weighs 1000 kg then total weight of box + truck can be calculated by just simply adding 10 and 1000 which will be 1010 kg.

## Vector Quantities

A Physical Quantity which has magnitude as well as direction is called a Vector Quantity or Vector.

Symbol for denoting Vector Quantities are usually written as a letter with an arrow on top pointing towards right or sometimes just bolded letter without an arrow on top.

Examples of Vector Quantities are force, velocity, acceleration, momentum and so on. The magnitude os a Vector indicates how small or large vector is and its direction indicate in which direction its point or being applied.

Moreover Vector Quantities cannot be added, subtracted, multiplied or divided with just using simple ordinary laws of algebra. We need to use specific **Vector Algebra** rules for this, because of direction.

## Difference between Scalar and Vector Quantities

Scalar Quantites | Vector Quantities |
---|---|

Have no direction | Have a direction |

Can be added, subtracted, multiplied or divided using simple laws of algebra | Need to use Vector Algebra rules for adding, subtracting, multiplying or dividing |

Symbol is denoted without an arrow on top | Symbol is denoted with an right pointing arrow on top or just letter is bolded |

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