|Vector is important to learn physics|
Suppose you are in a field in summer day think about the temperature you are feeling in field around you temperature in all direction east ,west,north,south will be same you will feel you can’t feeling different temperature in any direction so temperature is independent of direction hence it is a scalar quantity means no direction for temperature now you want to go to your home from field at this moment you have to decide a direction for your home destination there may be many road which connect to your home but there may be only one single smallest straight line path connecting position of your home and your current position in field which will give a single direction after connecting two position this is called displacement which is having a direction hence it is called vector quantity, what about other road or path connecting to your home all are distance having no specific direction many times direction will change which is independent of direction only depend upon path length hence it is vector quantity.
Now take other example suppose you are in the center of the same field, i told you hey Jon one gold bag is at a distance of 50 m please brought quickly suppose you are not seeing that gold bag from your position think what you will do ? if you are intelligent you will run 50 m radius of circle to find that bag and you will get gold bag somewhere circumference of circle radius 50 m and the you will brought but it will take more time game is over.
suppose for gold bag if i give you direction 30 degree with east you will reach exactly position of gold bag and brought quickly hence you can think the power of direction means vector, have you ever think how computer brought your data quickly due to this vector power data are storage in magnetic field which is a vector quantity directly point to exact location of data and fetch quickly.
Representation of vector: A vector quantity is represented by arrow → remember arrow is not a vector it is only representation quantity is vector arrow gives three information about quantity first direction, second magnitude, third point of application.
see in both the above cases all three parameter are different
direction – different ( first case right, second case left )
magnitude – different (length of arrow first case magnitude less, second case magnitude large )
point of application ( first case on hand and in second case knee )
this vector may be any quantity like force, velocity, displacement.. arrow gives only three information.
Unit vector : Unit vector is a vector having unit magnitude means one in the same direction of original vector every vector has a unit vector then it is made as long as we want it is very powerful vector which help to solve many difficult problem see below representation .
Suppose a bus is going with velocity of 5 m/s in east direction
5 m/s →
→→→→→ towards east V𝖇 this is full vector representation
unit vector representation
1 m/s ∧
→ towards east V𝖇 and also this can be written as
∧ → →
V𝖇 = V𝖇/⎥ V𝖇⎥ unit vector = vector/magnitude
Unit vector in Cartesian coordinate system
We have already study in previous post Cartesian coordinate system x,y,z axis are called Cartesian coordinate system three axis six direction considering positive and negative direction
now unit vector along x axis is i cap ( cap = ^)
unit vector along y axis is j cap
unit vector along z axis is k cap
what is advantage of writing this vector in i,j,k form it makes operation of vector easy addition, subtraction, multiplication and division with similar quantity i,j,k this is main advantage .
with the help of unit vector we can find position of any point in space or 3-D easily following the root of x, y, z axis hence any point suppose p(2,3,5) located in space then we can write this position vector in unit vector form suppose o is origin o(0,0,0)
op = r = (2-0)i^ +(3-0)j^+(5-0)k^
r = 2i^+3j^+5k^
where r is full vector and i^, j^, k^ are unit vector similarly any other point can be written as
r₁ = 2i^+3j^-5k^, r₂ = 2i^-2j^-3k^ now here it is easy to make operation between r,r₁,r₂ vector without using unit vector it was difficult to make operation between r,r₁,r₂ now this can be any vector quantity like displacement, velocity, acceleration, force .
now for magnitude calculation for such type of unit vector
suppose r = ai^+bj^+ck^ then its magnitude will be written as
|r| = ⎷a²+b²+c² under root square of the a,b,c
Equal vector condition:
Two vector are called equal if and only if having equal magnitude and same direction .
→ here A vector and B vector are equal
Negative vector: having equal magnitude in opposite direction
Col linear vector : vector having same direction but different magnitude
Co planer Vector : vector in same plane having different magnitude and direction
A →→→→→→ B
Null Vector or Zero Vector: Vector having Zero magnitude but having direction a point is a null vector or zero vector here its magnitude is zero then what is direction answer is any direction a point has any direction simply add two opposite vector what will be result its magnitude will be zero null since it is a vector addition hence result will be also a vector pointing towards any direction.
addition and subtraction of null vector with other vector not effect vector but multiplication becomes zero.
Important : what is difference between A and |A| here simple A indicate that quantity is scalar only magnitude but |A| indicates it is a vector quantity but we are only interested for magnitude this is the difference . there all vector having great application in whole physics we will study latter where vector concept will be very important so focus ton command over vector and be yourself as vector direction to reach your destination.
thanks for learning Vector is important to learn physics
dated 26th May 2018