Question

Guys Explain as if i dont know anything.....
1. Vectors, its addition ....etc laws.
2. Newtons laws of motion (11th base)

Answer 1

Hi there,

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Take it easy.....

cause this is gonna b a breeze ...  :)

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1. Vectors...

well ... you might b confused as to what this is... but when u understand.. ull' come to light...

there are two types of physical quantities.... and by physical quantities .. I mean the various kinds of dimensions we have around us.... like length, area..... current etc..

the two types of physical quantities are scalars and vectors....

1)scalars are those quantities which have only magnitude(only a value)

 say... temperature..... or time... ... speed... or distance... etc....

by no means can you assign a specific direction for these quantities as they are just merely values....

2) vectors are directed physical quantities...  say displacement, velocity ... acceleration...

for all these.. you can assign a particular direction in which it is acting....

for this purpose of direction ... we have a 3D coordinate system (cartasien) in which x, y, and z directions are denoted by i, j, and k vectors....

if u see a cap. i.e; '^' over any of these letters.... it means that they are unit directions...

a combination of all these three directions gives rise to a vector.... which is supposedly to start at one point(tail of the vector) and end at another(head)... both these points are merely the normal 3D coordinates....

****.. and to represent a vector in terms of these coordinates we subtract the head coordinates from the tail.... ****

for representation of vectors.. there are two ways....

1) linear representation...  

 (a i + b j + c k)

where a, b ,and c are the difference in the x y and z coordinates of the head and tail....

even though there is a + sign... we cant add them as they are all different directions....

2) Matrice representation (I would strongly recommend this method for u to                

                                            understand better)

Say we have a random vector v(bar)   i.e there is a bar over the letter to indicate that it is a vector....

v = $\left[\begin{array}{ccc}a\\b\\c\end{array}\right]$

compare this with the linear and u will find out that the 1st row is the i drxn and second row is the j  drxn and so on...

it is easier as you dont get confused and mix i j and k....

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say you have a 3D cartesian system and you want to represent a vector which starts at the origin and ends at (1,0,5)..

simply do this by subtracting head from tail coordinates

i.e

v(vector)=

$\left[\begin{array}{ccc}1\\0\\5\end{array}\right]$ - $\left[\begin{array}{ccc}0\\0\\0\end{array}\right]$

= (1 i +0 j + 5k)

where the respective rows represent i, j and k///...

to find the magnitude(i.e; the length of the vector) just take the square root of the square of all directions i, j, and k,

|v|=√(a²+b²+c²)

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addition and subtraction of two vectors is simple.... when you have two vectors represented in the matrice form ... just add them...

... as for the laws... there are two... the second being a symmetric modification of the first.

1) triangle law....

states that the sum of the vectors when taken in order... i.e; joined head to tail in a triangle is zero...  

say you have 2 vectors a and b...

add them to get c which will be the closing side of the triangle....

2) the parallelogram states that the resultant of the two vectors making an angle Ф with each other will b the principle diagonal of the parallelogram whose magnitude is given by

|v| = √(a²+b² + 2abcosФ)

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for scalar product (indicated by a '.')

say you have two vectors in matrice form and wanna find scalar product...

you can do so by directly multiplying same drxns and adding the rest..

  $\left[\begin{array}{ccc}1\\1\\1\end{array}\right]$ .

  $\left[\begin{array}{ccc}2\\2\\3\end{array}\right]$ = 2+2 + 3 =7 and the drxns i, j , k dissapear because it is a scalar product.

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for vector cross product do the normal criss cross method as indicated in your text...

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NLM/// pls... ask as separate question...

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cheers// :)

Answer 2

Answer:

vectors meaning

the quantity which has direction as well magnitude

newton's law of motion

first law

when we state at the rest or at uniform motion unless compelled to change that state by an applied unbalanced.

third law.

every action there is an equal and opposite reaction