A quantity is a characteristics of a body that can be measured with an instrument. Examples are length, area, temperature and so on.
All these quantities can be divided into two types: Scalar and Vector quantities. Normally it is quite easy to deduce whether a quantity is a scalar or a vector quantity but of you have any difficulties a list will be given later on.
Let us see how to identify a vector and a scalar quantities.
A scalar quantity is one that has a magnitude and a unit.
Remember the magnitude of a quantity is a number that represent its size.
Examples of scalar quantities are length, mass, temperature, etc
length = 19 m
mass = 4 kg
As you can see these quantities can only be represented by a magnitude and a unit.
A vector quantity is one that has a magnitude, a unit and a unit.
Examples of vector quantity are acceleration, force, velocity, etc.
velocity = 100 km/h towards the north
Displacement = 100 m eastward
Force = 10 N 300 to the horizontal
As you can see all quantities that can be represented using an arrow and in which a direction make sense is a vector quantity.
For example a mass will not make sense with a direction hence it is a scalar quantity. A force make sense with a direction hence it is a vector quantity.
How to know whether a quantity is a vector or a scalar quantity
- In case you do not know that a quantity is a scalar or a vector then you can consult this list[under construction]
- Two quantities can be added or subtracted from each other unless they are both scalar or vector quantities. And the answer is a scalar
Hence if A = B –C
and C is a scalar quantity then B must be a scalar quantity and as a result A must be a scalar quantity. The same reasoning would have applied if addition was performed.
- If two quantities A and B are multiplied to get quantity C as in C = A*B then the nature of the quantity C would vary according to the table below.
|Scalar||Scalar||Scalar||Mass = density *volume|
|Scalar||Vector||Vector||Velocity = time *acceleration|
- If a quantity A is divided by another quantity B to obtain quantity C as in C = A/B then then the nature of quantity C would vary according to the table below.
|Scalar||Scalar||Scalar||Density = mass/volume|
|Vector||scalar||Vector||Acceleration = Velocity /time|
|Vector||Vector||scalar||time = velocity /acceleration|