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## Tuesday, November 24, 2009

### Scalar and vector quantities

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.

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.

Vector quantities

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.

 A B C Example Scalar Scalar Scalar Mass = density *volume Scalar Vector Vector Velocity = time *acceleration vector Vector

• 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.
 A B C Example Scalar Scalar Scalar Density = mass/volume Vector scalar Vector Acceleration = Velocity /time Scalar vector Vector Vector scalar time = velocity /acceleration

1. is ACCELERATION VECTOR OR SCALAR

2. Indeed acceleration is a vector quantity,

The reason why acceleration is a vector quantity is that an acceleration is created by a force. A force is a vector quantity in that a force must act in a particular direction and it must have a direction.

Since the force will cause acceleration in a particular direction it will act in the same direction as the force and as a result it will be a vector quantity.

3. This is among the best I ever got.

4. Thank you very much for this very informative article.
Pls from what u wrote can we say generally that:
scalar*scalar=scalar
scalar*vector=vector
vector*vector=vector
whether * represents multiplication,addition, subtraction or division.
Thank u!

5. Note that for multiplication of two vector quantity it is slightly more difficult. I will come back to it in a later post