Saturday, 3 March 2018

Basic Concept of Vector and Scalar

Basic Concept of Vector and scalar

Hello Friends,
Today our topic is very important for physics Vector it is said physics can be teach through two method one is vector and other is calculus, vector method is easy to teach and learn so you can understand the importance of vector all important physical quantity in physics are vector without vector physics is poor.In previous post we have discussed some little about Vector, this is topic of mathematics but we study in physics because mathematics is tool of physics just like Gun is arms of soldier mathematics is arms for physicist lets start.

Basic Concept of Vector and Scalar
Basic Concept of Vector and Scalar

Coordinate system: very first we will study what is coordinate system suppose you go to college or office every day on your birthday you invite your friend to join your birthday party then your friend ask you how much distance is your home from college then how you calculate distance of your home from your college ? simple there are always two point to calculate distance between them here your college and your home if you want to calculate distance from college to home then you fixed the origin (not moving point ) at your college as reference point and calculate distance from college to home in other case you can take home as fixed point and can measure the distance from home to college in both the cases distance will be same hence you are free to take any point as reference point but condition is the fixed origin point should not move that is called inertial frame of reference so we must required a frame of reference point to measure distance without frame of reference we can't calculate any body or particle position on the earth or in universe so in mathematics we take x,y,z coordinate system as frame of reference point its coordinate value taken as (0,0,0) at origin fixed to locate any body or particle position if once the body position is known then we can calculate distance or displacement of the body or particle distance gives magnitude of length like 10 km, 20 km , 100 km ... as in above figure shown        
Direction of Physical quantities : direction of physical quantity me be in any direction like left, right, up, down, at an angle so it specify the particular direction of quantity and it is very important to know the direction of physical quantity otherwise we will not get the desired result whether you are moving but you will not reach at your destination now we can make definition of vector and scalar quantities .
Vector quantities : vector quantity is that physical quantity which has magnitude as well as direction magnitude fixed the quantity, direction specify the quantity and also follow the triangle law of vector addition compulsory magnitude, direction, vector addition law, suppose on an office door written pull and you want to inter in the office and you are applying force and pushing the door with a great force but you will be unable to open the door, see open the door we need force and force is a vector quantity direction and magnitude both is important here you are applying force but in wrong direction so you will not be reach at your destination here you have to apply the force in right direction that is pull so direction is very very important for vector quantity, some example of vector quantities, force, displacement, velocity, acceleration, momentum, torque and many more  here direction is associated with each physical quantities without direction quantity will not be specify.
Scalar quantities : scalar quantities are those quantities which has only magnitude no direction and not follow triangle law of addition it has only and only magnitude suppose in summer day you are in a field you are told to ask the temperature you are feeling you will say hotter feeling 50⁰ C in all direction of field here temperature has no any specific direction in field so it is independent of direction next example suppose in a sack 50 kg rice is filled and packed if i ask the mass of rice you will told 50 kg, you will not told 50 kg in left, right, up, down because it does not make any sense only 50 kg rice in the sack so scalar quantities are not associated with direction some example of scalar quantities are mass, temperature, time, distance, speed, work, power, energy many more not associated with direction one more type of quantity is called tensor which we not need to study here which is neither vector nor scalar. 
Representation of vector by symbol :
suppose we want to write mass of rice = 50 kg for this we simply not write as much of language actually we take a symbol and write  a = 50 kg where a represent mass of rice take other example temperature of room = 30⁰ C for this we write simply
T  =  30⁰ C  where T represent temperature of room generally we use symbol for physical quantity representation benefit of this is only write short with symbol there all are example of scalar quantities but for vector quantity see how we write ?
→10 N   c = 10 N towards right where c represent force we defined a symbol  →20 N towards right  d  = 20 N towards right  but this type of writing is not good vector quantity has direction and it is very important properties of vector quantity so we want to write vector quantity some different symbol which can distinguish from other scalar quantity and after seeing the symbol we can well recognize this is vector quantity as we know there are two type of quantity one is vector and other is scalar in similar way girls are of two type one is married and other is unmarried and we easily recognize married girls used vermilion  hence for vector we use arrow symbol to recognize easily this is vector quantity hence vector is represented     → 
                                      c   = 20 N towards right .
  💃 →20 N            10 N ←💃                 💃
   f₁                                      f₂                   ↓ f₃
                                                                 5 N 
See here how we will write force for each case f₁, f₂, f₃ 
→                                      →                                   →
f₁  = 20 N towards right , f₂  = 10 N towards left , f₃  = 5 N down
important point arrow above symbol indicate only about vector not direction arrow always written above symbol is left to right whatever be the force direction its always written left to right never write right to left for vector representation 
arrow on symbol indicate we are talking about vector does not gives direction .                            ←        ↑             
wrong vector representation       f₂ ,     f₃            f₃
                    →                                                             ↓
if we write  f  = 10 N towards right  here 10 N represent magnitude and towards right represent direction.
there are many situation were we are only interested in magnitude in that case we write          →
                                        ⎟ f ⎥   = 20 N   this means we are only interested in magnitude not considering direction or this can be also written as f  = 20 N here arrow above symbol is removed only taking magnitude .

       Some time we write vector as below  
     (Tail)p →→→→→→→→→→→→→→ q (head)
     now we can represent as vector    → 
here we can always write first tail then head we can't reverse since direction always goes from tail to head .
Some new physical quantity :
Position :  its mean where an object is located suppose in a cricket ground some body ask where is Sachin ? its mean that what is position of Sachin in cricket ground some body answer position of Sachin is 5m from batting crease, is this information is sufficient  for locating Sachin position in the ground  answer is big no                                   💃
                                       █→          💃         
Here Sachin can be in any direction 5m from batting crease so this information is insufficient to locate exact position of sachin so for exact position we must required direction to locate exact position hence position is a vector quantity associated with direction .
if some body ask where is sachin in ground and other person say sachin is 5m distance this statement is also insufficient from where he is 5m distance it may be from batting crease, from pavilion, from bowling point, from anywhere else hence you have to specify from where he is 5m distance. if you say from batting crease then here batting crease is reference point or it is also called origin hence origin is required to talk about position now position is vector quantity so for its direction we take x-y axis 
                               ↑           q
                               ↑                           p
now we can locate any point on x-y plan like point p and point q opposite of x axis is negative and opposite of y axis is also negative now for position we subtract final position coordinate minus initial position coordinate like x  =x₂  - x₁   , y  =  y₂   -  y₁   
→                             →                                 →
r   = (x₂  - x₁)i    + (y₂   -  y₁)j 
this position is written in vector form where r vector represent position this will provide exact position of any body or particle in plan . thanks for reading Basic Concept of Vector and scalar.
dated 19th May 2018

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