Scalar and Vector Quantities

In order to express these measurements of Physical Quantities, we can use Scientific Notation according to which
100000000 can be written as 108
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.

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.

\begin{equation} \vec{F} \text{ for denoting force vector} \\ \vec{v} \text{ for denoting velocity vector} \\ \textbf{Or} \\ \textbf{f} \text{ for denoting force vector} \\ \textbf{v} \text{ for denoting velocity vector} \\ \end{equation}

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 QuantitesVector Quantities
Have no directionHave a direction
Can be added, subtracted, multiplied or divided using simple laws of algebraNeed to use Vector Algebra rules for adding, subtracting, multiplying or dividing
Symbol is denoted without an arrow on topSymbol is denoted with an right pointing arrow on top or just letter is bolded
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