Vectors

  Very often in your daily life , you come across measurment the process of measuring something i.e either it be your table cloth length or it be length of a national highway , you may be weighing apples (let say 5kg). It's all okay . Let me put you in a situation when you are driving on a national highway and someone ask you how far away the Delhi is from Agra, you may say around 200km but when they ask stepwise how will i upto there . You may say like 10 km on this highway then north again after 30 km on the way you have to take right and bitwise you will cover the distance .

      The breakdown factor of science or the most manipulating factors in science is vector i.e the quantity that require both magnitude and direction for it's complete descreption .Before starting anything let's do something of co ordinate .

 When we say 20m east it means 20 m in this direction -------------> . When two no lines that are  mutually orthogonal are intersected the point of inyersection is origin right to that is east or x -cordinate left to thet is x'-cordinate . And similarly y is upward and y' is downward .

   Now , say you are in xy-plane and you have to arrive at (3,4) how you will come across to it . Two method 

you go 3 units right then 4 units up. A unique point is defined at that point ,i.e (3,4)

You calculate distance between origin and (3,4).,you take a rotating positon vector of length 5 unit (distance is 5 unit) then rotate at a suitable unique angle 

 

 Vectors are represented by either a bold letter or an arrowhead avobe it 

Like , a vector defined from o to a is either A  OR A^

So from both methods you will come to an unique point (3,4)

Let i, j ,k be the unique unit vector along the co ordinate axis ..

So when yo come to point it can be distributed and written as  

A= x i^+yj^=3i^+4j^

Now vector can't be normally  added 

They are added by traingle law of addition this state that 

If two vectors are represented by two adjacent sides of traingle in a order then another sides of traingle which is opposite in order represent the sum .

Another thing is 

Product of vectors 

1 scalar multiplication 

That is normal multiplication by k of a vector is k times of vector 

Another is like dot and cross product 

Dot product : product of two vector is scalar 

Vector product : product of two vector is vector whose direction is oerpendicular to both tha planes of both vector

I.e all about vector

Another is ...

Some concequences work done like .

When you move perpendicular to direction of force is zero ...

I.e all about vector 

You may consider

Concept of physics (H.C VERMA)

 university physics 

Reshnik halliday walker

FOR more information and problem practice ....