Scalar and Vector Quantities - Param Himalaya Physics

Scalar and Vector Quantities ? - Param Himalaya Physics

What is a scalar Quantity ? It's example :

A Physical quantity which is described completely by its magnitude or size is called a scalar quantity. Thus a scalar quantity has only magnitude and no direction.

Example of scalar quantities
Length , Distance , Area , Volume , Mass , Time , Power , Energy , Speed , temperature etc.

Characteristics of scalar quantities :

  1. A scalar quantity can be represented by a number with proper units. The number represent the magnitude of the quantity. Example : 2 Kg. Here 2 is number and Kg is unit.
  2. The scalar quantities having similar units get added or subtracted by the usual rules of arithmetic. Example : 2m + 3m = 5m.

What is a vector quantity? It's example

A physical quantity which requires both magnitude ( or size ) and direction for its complete description is called a vector quantity. Thus , a vector quantity has both magnitude and direction.

Example of Vector Quantities: 

Displacement , velocity , Acceleration , Force ,Weight , Momentum etc.

Characteristics of Vector Quantities:

1. Representation of a vector : A vector quantity can be represented by a number with proper units and a direction. 
Example : 45 km/Hour toward south.
Here 45 - Number magnitude , KM/ Hour - Unit , South - Direction.
2. Notation : vector are written either in bold letters or as the letters having an arrow over them. A or A
3. The vector quantities having similar units but different directions are not added/ subtracted by ordinary arithmetical rules. If two or more vector quantities have the same units and the same direction, then their magnitudes get added/ subtracted by ordinary arithmetical rules.

How is a vector quantity shown graphically ?

A vector quantity can be represented graphically by an arrow where 
* The length of the arrow represents the magnitude of the vector quantity.
* The arrowhead represents the direction of the vector quantity.
Graphical representation of displacement - param himalaya


To show a vector quantity graphically , we should have the following information: 
* The magnitude of the vector quantity
* The direction of the vector quantity.

Question: show a displacement vector of 2.5 m towards 30° west of North on a scale , 1 cm = 1 m.
Answer : we have 1 m = 1 cm 
So , 2.5 m = 2.5 × 1 cm = 2.5 cm
Graphical representation of displacement - param himalaya


This means the vector can be shown graphically by a line of 2.5 cm in the direction 30° west of North. Thus , the displacement vector is respresented by the arrow OA.
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