wikimama Class 12 ch 12 3-D

8/4/2019 wikimama Class 12 ch 12 3-D

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=

:B#GIKCIRT\Zrtmlgnr alfi lf rntii blcifzlkfz

M zrtmlgnr alfi lf zxmji lz yfl}yia| biritclfib le

.l, Lr xmzziz rntkygn m gluif xklfr mfb nmz m gluif bltijrlkf! kt

.ll, Lr xmzziz rntkygn rwk gluif xklfrz&Jmtrizlmf Ektc0

= = =

= 4 :

~ ~ | | p pd d d

I}ymrlkfz mdkui lz mazk jmaaib rni z|ccirtljma ektc ke rni zrtmlgnr alfi! mfb tixtizifr mzrtmlgnr alfi rntkygn rni gluif xklfr .~ =! | =! p=,! wnkzi bltijrlkf tmrlkz mti d =! d4 mfb d : &

Ekt m 3 8! zk t d mfb lrz Jmtrizlmf ektc lz= 4 :

~ | pd d d

Lf i}ymrlkfz mdkui! d =! d4! d : mti rni bltijrlkf tmrlkz ke rni zrtmlgnr alfi& I}ymrlkfz ke rni zrtmlgnr alfi! rntkygn rni xklfr X.~ =! | =! p=,! wlrn bltijrlkf

jkzlfi a! c! f mti = = =~ m | | p p

a c f&

Rni gifitma jkktblfmriz ke m xklfr kf m alfi mti gluif d| .~ = / at! | = / ct! p = /ft, wniti t lz rni blzrmfji dirwiif xklfr .~ =! | =! p=, mfb rni xklfr wnkzijkktblfmriz mti rk di wtlrrif&

I}ymrlkf ke m zrtmlgnr alfi rntkygn rwk gluif xklfrzJmtrizlmf Ektc0

= = =

4 = 4 = 4 =

~ ~ | | p p~ ~ | | p p

Rnlz lz rni Jmtrizlmf i}ymrlkfz ke rni alfi xmzzlfg rntkygn rni xklfrz .~ =! | =! p=, mfb.~4! | 4! p4,&Jkaalfimtlr| ke rntii xklfrz

Air M! D! J di rntii gluif xklfrz wlrn xkzlrlkf uijrktz m! d mfb j

tizxijrluia|&

= =

: :

o ow y = u y .= ,u

o o

! wniti 3 =:

oo

&

Nifji J wlrn xkzlrlkf uijrkt j lz jkaalfimt wlrn M mfb D& Wi jkfjaybi rnmr rntii xklfrzmti jkaalfimt le rniti i~lzrz m alfimt tiamrlkf dirwiif rnic! zyjn rnmr rni zyc ke rnijkieeljlifrz lf lr lz pitk&

Rntii xklfrz wlrn xkzlrlkf uijrktz m! d! j

wlaa di jkaalfimt le rni uijrktz

d m j mmfb

mti xmtmaaia& Wi cm| mazk yzi rni zijrlkf ektcyam& Le kfi ke rni xklfrz blulbiz rni alfi

zigcifr! `klflfg rni ticmlflfg rwk! lf m bielflri tmrlk! rnif rni gluif xklfrz wlrnxkzlrlkf uijrktz m! d! j

mti jkaalfimt& Lf rni xtizifr jmzi! air


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4

4 3 9f 2c 8 f :c! = f 4cc f c f

wnljn mazk zmrlzeliz : 3 9f cc f

&

Mfgai dirwiif rwk alfizJmtrizlmf Ektc0 Le M .~=! | =! p=,! J .~ 4! | 4! p4, di rni rwk gluif xklfrz mfb

= 4 : = 4 :

d d l d ` d o! b b l b ` b o

di rni gluif uijrktz& Rni mfgai dirwiif rni alfizlz gluif d|

jkz 3 = = 4 4 : :4 4 4 4 4 4= 4 : = 4 :

d b d b d b

d d d b b b&

Le a=! c =! f =? a4! c 4! f 4 mti rni bltijrlkf jkzlfiz ke alfiz! rnif jkz 3 a=a4 / c =c 4 / f =f 4& Rni alfiz mti xitxifbljyamt .kt ktrnkgkfma, le d =b=/ d 4b4/ d : b : 3 8 kt a =a4 / c =c 4

/ f =f 4 3 8&

Rni alfiz mti xmtmaaia le := 4= 4 :

dd db b b

kt a= 3 a4! c = 3 c 4! f = 3 f 4&

Znktrizr blzrmfji dirwiif rwk alfiz

Jkfzlbit rwk alfiz A = mfb A4 lf zxmji& Le rni rwk alfiz bk fkr lfritzijr mfb mti fkrxmtmaaia! rnizi alfiz mti jmaaib zoiw alfiz&

Le rni alfiz A = mfb A4 mti tizxijrluia|= = =

= = =

~ ~ | | p pa c f

mfb 4 4 44 4 4

~ ~ | | p pa c f

!

rni jkfblrlkf ekt lfritzijrlfg alfiz dijkciz

= 4 = 4 = 4

= = =

4 4 4

~ ~ | | p pa c f 8a c f

&

Rni alfiz A = mfb A4 mti zoiw le= 4 = 4 = 4

= = =

4 4 4

~ ~ | | p pa c f 8a c f

&

mfb rnif rni znktrizr blzrmfji dirwiif A = mfb A4 lz

4 = 4 = 4 =

= = =4 4 44 4 4

= 4 =4 = 4 = 4 = 4 4 =

~ ~ | | p pa c fa c f

.a c c a , .c f f c , .a f a f ,&

Le mf| zrtmlgnr alfi lz gluif lf gifitma ektc rnif lr jmf di rtmfzektcib lfrkz|ccirtljma ektc mfb wi jmf xtkjiib eytrnit&

XAMFI


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4/7

2

Ialclfmrlfg m! d! j etkc rnizi i}ymrlkfz! wi kdrmlf rni i}ymrlkf ke rni xamfi jkfrmlflfg

M! D! J mz= = =

4 = 4 = 4 =

: = : = : =

~ ~ | | p p~ ~ | | p p 8~ ~ | | p p

&

I}ymrlkf ke m xamfi xmzzlfg rntkygn m xklfr mfb xmtmaaia rk rwk gluif alfizJmtrizlmf ektc0

Air rni xklfr M di .~ =! | =! p=, mfb air rni bltijrlkf tmrlkz ke rni gluif alfiz di .d =! d 4! d : ,mfb.j =! j 4! j : ,& Nifji rni i}ymrlkf ke xamfi xmzzlfg rntkygn m xklfr mfb xmtmaaia rk rwkgluif alfiz lz

= = =

= = :

= 4 :

~ ~ | | p pd d d 8j j j

&

Le m xamfi jkfrmlfz rni alfi = = =

= 4 :

~ ~ | | p pd d d

mfb lz xmtmaaia rk rni alfi

4 4 4

= 4 :

~ ~ | | p pj j j

rnif maa rni xklfrz ke rni eltzr alfi wlaa di a|lfg lf rnlz

xamfi& Cktikuit! rni xamfi wlaa di xmtmaaia rk dkrn rni alfiz& Nifji rni i}ymrlkf

ke rni xamfi lz= = =

= = :

= 4 :

~ ~ | | p pd d d 8j j j

Rwk alfiz mti jkxamfmt le m xamfi jmf di btmwf rk jkfrmlf dkrn rni alfiz&Xamfi xmzzlfg rntkygn rni lfritzijrlkf ke rwk gluif xamfizLf Jmtrizlmf z|zric! rni i}ymrlkf ke m xamfi xmzzlfg rntkygn rni lfritzijrlkf ke rnixamfiz

m=~ / d =| / j =p 3 b = mfb m4~ / d 4| / j 4p 3 b 4 lz m=~ / d =| / j =p b= / .m 4~ / d 4| / j 4p b 4, 3 8&

Rwk xamfiz lfritzijr lf m alfi& Nifji rni i}ymrlkfz m =~ / d =| / j =p 3 b = mfb m4~/ d 4| / j 4p 3 b 4 rkgirnit tixtizifr m alfi&

I}ymrlkf ke rni xamfi rntkygn m gluif alfi0

.l, Le rni i}ymrlkfz ke m alfi mti gluif lf gifitma ektc mzm=~/d =|/j =p/b =383m 4~/d 4|/j 4p/b 4! rni i}ymrlkf ke xamfi xmzzlfg rntkygn rnlzalfi lz .m =~ / d =| / j =p / b =, / .m 4~ / d 4| / j 4p / b 4, 3 8&

.ll, Le i}ymrlkfz ke rni alfi mti gluif lf z|ccirtljma ektc mz = = =~ ~ | | p pa c f

!

rnif i}ymrlkf ke rni xamfi lz m.~ ~=, / d.| | =, / j.p p =, 3 8! wniti m! d! j mtigluif d| ma / dc / jf 3 8&

Mfgai dirwiif rwk xamfiz

Air = =

t f x mfb 4 4

t f x di rwk xamfiz& Rni mfgai dirwiif rni xamfiz lz zmci mzrni mfgai dirwiif rnilt fktcmaz& Nifji mfgai dirwiif rni xamfiz lz gluif d|


5/7

9

jkz 3 = 4

f f &

Lf jmzi! uijrktz = 4F Fmfb

makfg rni fktcmaz .kt bltijrlkf tmrlkz ke rni fktcma, mtigluif! rnif

jkz 3 = 4= 4

F F

q F q q F q

&

Rni xamfiz mti xitxifbljyamt le 34

= 4F F 8

&

Rni xamfiz mti xmtmaaia le = 4

f f Mfgai dirwiif rni xamfiz m =~ / d =| / j =p / b = 3 8 mfb m 4~ / d 4| / j 4p / b 4 3 8

lz = = 4 = 4 = 44 4 4 4 4 4= = = 4 4 4

m m d d j jjkz

m d j m d j&

Le m=m4 /d =d4 /j =j 4 3 8! rnif rni xamfiz mti xitxifbljyamt rk imjn krnit&

Le = = =4 4 4

m d jm d j

rnif rni xamfiz mti xmtmaaia rk imjn krnit&

Mfgai dirwiif m alfi mfb m xamfi

Air rni i}ymrlkf ke rni alfi di t m d

mfb rnmr ke rni xamfi

t f x !

f lz m yflruijrkt makfg rni fktcma rk rni xamfi& Air yz btmw m xamfi rntkygn rni gluif alfi wnljn lzxitxifbljyamt rk rni gluif xamfi& Air A di rni alfi ke lfritzijrlkf ke rnlz xamfi wlrn rnigluif xamfi& Rni mfgai dirwiif rni gluif alfi mfb A bielfiz rni mfgai dirwiif rnigluif alfi mfb rni gluif xamfi&Air di rni mfgai dirwiif rni gluif alfi

mfb rni fktcma rk rni xamfi& Rnif jkz 3d fq d q

&

Le lz rni mfgai dirwiif rni gluif alfi mfb

rni gluif xamfi& rnif 34

zlf 3

jkz 3

d fq d q

&

Le F lz m uijrkt makfg rni fktcma rk rni

xamfi! rnif zlf 3 d Fq d q q F q

&

d f

A


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Le rni i}ymrlkf ke m xamfi lz m~ / d| / jp / b 3 8! rnif bltijrlkf tmrlkz ke rni fktcma rk

rnlz xamfi mti m! d! j& Le rni i}ymrlkfz ke rni zrtmlgnr alfi mti = = =~ ~ | | p p

a c f!

rnif mfgai dirwiif rni xamfi mfb rni zrtmlgnr alfi lz gluif d| zlf 34 4 4

ma dc jf

m d j

&

Xamfi mfb zrtmlgnr alfi wlaa di xmtmaaia le ma / dc / jf 3 8

Xamfi mfb zrtmlgnr alfi wlaa di xitxifbljyamt le m d ja c f

&

Rni alfi wlaa ali lf rni xamfi le ma / dc / jf 38 mfb m~ = / d| = / jp = / b 3 8&Blzrmfji ke m xklfr etkc m xamfi

Jkfzlbit m xklfr M wlrn xkzlrlkf uijrkt m mfb m xamfi wlrn i}ymrlkf

t f x & Btmwxamfi rntkygn M mfb xmtmaaia rk rni gluif xamfi&I}ymrlkf ke rni xamfi lz

.t m, f 8

kt

t f m f & Etkc elgyti!

MC 3 FA3 KF KA3

m f x Nifji blzrmfji ke rni xklfr M etkc rni gluifxamfi

3 qMCq 3

q m f x q&

K

M.m,

f

A C

F

m

Lf jmzi rni i}ymrlkf ke rni xamfi lz M~ / D| / Jp 3 B

kt t F B t F Bq Fq q Fq

!

rni blzrmfji ke M.m, etkc rni xamfi lz

= = =4 4 4

M~ D| Jp BF B m F Bm

q F q q F q q Fq M D J

! wniti = = =

m ~ l | ` p o&

Xkzlrlkf ke m Xklfr w&t&r& m Xamfi0

Rwk xklfrz X.~ =! | =! p=, mfb ].~ 4! | 4! p4, ali kf rni zmci kt kf rni kxxkzlri zlbiz ke m

xamfi m~ / d| / jp / b 3 8 mjjktblfg mz m~ = / d| = / jp = / b mfb m~ 4 / d| 4 / jp 4 / b mtike rni zmci kt ke rni kxxkzlri zlgfz& Rni xamfi blulbiz rni alfi `klflfg rni xklfrz X mfb] i~ritfmaa| kt lfritfmaa| mjjktblfg mz X mfb ] mti a|lfg kf rni zmci kt rni kxxkzlrizlbiz ke rni xamfi&

Rni blzrmfji dirwiif rwk xmtmaaia xamfiz lz rni magidtmlj bleeitifji kexitxifbljyamt blzrmfjiz ke rni xamfiz etkc rni ktlglf&

Dlzijrkt Xamfiz ke Mfgai dirwiif rwk Xamfiz0


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Rni i}ymrlkf ke rni xamfiz dlzijrlfg rni mfgaiz dirwiif rwk gluif xamfiz m =~ /d =| /j =p/b = 3 8 mfb m 4~ / d 4| / j 4p /b 4 3 8 lz

= = = = 4 4 4 44 4 4 4 4 4= = = 4 4 4

m ~ d | j p b m ~ d | j p b

m d j m d j&

Le mfgai dirwiif rni dlzijrkt xamfi mfb kfi ke rni xamfiz lz aizz rnmf 29 rniflr lz mjyri mfgai dlzijrkt krnitwlzi lr lz kdryzi mfgai dlzijrkt&

Le m=m4 / d =d4 / j =j 4 lz figmrlui! rnif rni ktlglf aliz lf rni mjyri mfgai dirwiifrni gluif xamfiz xtkulbib b = mfb b 4 mti ke rni zmci zlgf mfb le m =m4 / d =d4 /j =j 4 lz xkzlrlui! rnif rni ktlglf aliz lf rni kdryzi mfgai dirwiif rni gluifxamfiz&

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wikimama Class 12 ch 12 3-D