Scalar and Vector Quantities

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What are Scalar and Vector Quantities?

♦ On the basis of direction and magnitude physical quantities are categorized into two groups. they are ..
• 1. Scalar Quantity
• 2. Vector Quantities

♦ Scalar Quantity
◘ A Scalar quantity is a quantity that has _
• Only magnitude.
• But no Direction◘ Example
• Temperature
• Distance
• Energy
• Speed
• Power
• Density
• Volume
• Time
• Mass
• Electric Current
• Charge
• Pressure
• Work
• Specific Heat
• Frequency
♦ Vector Quantity
◘ A vector quantity is a quantity that has _
• Both a magnitude and a direction.
• It follows the vector algebra  rules for the performance of operations. e.g – triangle  law or parallelogram law of vector addition.◘ Example :-
• Velocity
• Displacement
• Impulse
• Magnetic Field
• Current density
• Electric Field
• Momentum
• Weight
• Force
• Acceleration
• Angular velocity

How to represent Scalar and Vector quantity

Scalar Quantity
•  The  quantity which is competely specified and defined by  a single number, along with the proper unit.

Examples
• The distance between two points [Example :- 25 Km]
• The temperature of a body [Example :- 100 0 C.]
• Time at which a particular event happened. [Example:- 18 Second]
• Mass of an object [Example:- 15 Kg]

Vector Quantity
•  The quantity which has both the magnitude and direction called a vector quantity.

• A vector quantity denoted  by – Bold face letter or symbol
• As an example, we can express the velocity vector as = v

• A vector is also represented by a bar or an arrow placed over the letter.
• As an example, we can represent the velocity vector as = ⊽

• Example of physical quantities that are represented by vectors are ….
* Velocity — 10 m/sec2, North
* Force — 10 N, South

• The magnitude of a vector is also represented by modulas function.
• The modulas value  often called absolute value.
• Indicated by |v| = v. (v = Velocity vector)
• The Mod value represent ony the magnitude of the vector not the direction of the vector.

Difference between Scalar and Vector quantities

Scalar Vector
It has only magnitude, but no direction. It  has both magnitude and direction.
Scalar quantity can divide another scalar quantity Two vector quantities cannot be divided.
Every scalar quantity is one dimensional. Vector quantity can be one (e.g UnitVector), two(e.g Force) or three dimensional (e.g Impuls).
Any changes in scalar quantity only affects  the magnitude of the quantity. Any Changes in vector  quantity may affect  the magnitude or direction  of the vector or both magnitude and direction may affected .
It follows the ordinary algebraic rules like addition, multiplication and subtraction It follows the vector algebra rules for the performance of operations.

 

Similarities between Scalar and Vector Quantities

•  A certain physical quantity is represented by both scalar and vector quantity.
•  Both have a specific dimension and unit.
•  By using a suitable instrument we can measure both the quantities.
•  Both the quantity holds a  certain finite magnitude.
•  Both scalar and vector quantities can be represented by a numerical magnitude  corresponding unit.
More Related Topics
Units and Measurements
Units / System of Units

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