8/4/2019 Wikimama Class 11 ch 12 3-D

http://slidepdf.com/reader/full/wikimama-class-11-ch-12-3-d 1/3

0

?A(MJLHJQY[

_qy`kmgq nkfj kf qgyjj akhjfklf

@ qy`kmgq nkfj kf s`oj k zfkpzjn{ ajqjyhkfja kb

'k+ Kq s`j qgylzmg ` mkrjf slkfq `fa g` ` mkrjf akyjoqklf. ly'kk+ Kq s`j qgylzmg q}l mkrjf slkfq&

Jpz`qklf lb ` qy`kmgq nkfj qgylzmg ` mkrjf slkfq @ `fa s`y`nnjn ql ` mkrjf rjoqly

i

&O`yqjk`f Blyh5

Njq qgj ollyakf`qj lb @ ij 'w0. {0. u0+ `fa qgj rjoqly i

ij k 9 ?˂ ˂ ˂i i k i e i d

& Njq S'w. {.

u+ ij `f `yikqy`y{ slkfq lf N& Qgjf ˂ ˂ ˂LS y wk {e ud

`fa k 0 0˂ ˂ ˂L@ ` w k { e u d

`fa

gjfoj jpz`qklf '0+ mkrj

0 0 0 0 9 ?˂ ˂ ˂ ˂ ˂ ˂ ˂ ˂ ˂wk {e ud w k { e u d 'i k i e i d+ 

80 0 0 9 0 ?

˂ ˂ ˂'w i +k '{ i +e 'u i +d &

Olhs`ykfm qgj oljbbkokjfq lb ˂ ˂ ˂k. e. d }j mjq

w 8 w0 $ i0. { 8 {0 $ i9. u 8 u0 $ i?&

Qgjj `yj qgj s`y`hjqyko jpz`qklf lb nkfj N& Jnkhkf`qkfm qgj s`y`hjqjy . }j mjq

0 0 0

0 9 ?

w w { { u u

i i i&&& '9+

Qgjj `yj qgj O`yqjk`f jpz`qklf lb qgj nkfj& Jpz`qklf '9+ `yj `nl o`nnja qgj

{hhjqyko`n blyh lb qgj qy`kmgq nkfj. `fa yjsyjjfq ` qy`kmgq nkfj qgylzmg qgj mkrjf

slkfq 'w0. {0. u0+. }glj akyjoqklf y`qkl `yj i0. i9 `fa i?&

 

Bly `

8 3. '0+ mkrj y i

 `fa kq O`yqjk`f blyh k

0 9 ?

w { u

i i i  • '?+

  Kf '9+ `fa '?+. i0. i9. i? `yj qgj akyjoqklf y`qkl lb qgj qy`kmgq nkfj&

  Jpz`qklf lb qgj qy`kmgq nkfj. qgylzmg qgj slkfq S'w0. {0. u0+. }kqg akyjoqklf

olkfj n. h. f `yj 0 0 0w ` { { u u

n h f&

  Qgj mjfjy`n ollyakf`qj lb ` slkfq lf ` nkfj `yj mkrjf i{ 'w0 $ ny. {0 $ hy. u0 $fy+ }gjyj y k qgj akq`foj ijq}jjf slkfq 'w0. {0. u0+ `fa qgj slkfq }gljollyakf`qj `yj ql ij }ykqqjf&

Jpz`qklf lb ` qy`kmgq nkfj qgylzmg q}l mkrjf slkfq

8/4/2019 Wikimama Class 11 ch 12 3-D

http://slidepdf.com/reader/full/wikimama-class-11-ch-12-3-d 2/3

9

Njq @ 'w0. {0. u0+ `fa I 'w9. {9. u9+ ij q}lmkrjf slkfq `fa njq qgjky slkqklf rjoqly ij

` `fa i

yjsjoqkrjn{& Qg`q k

0 0 0 9 9 9˂ ˂ ˂ ˂ ˂ ˂` w k { e u d. i w k { e u d

&

Njq S 'w. {. u+ ij `f `yikqy`y{ slkfq lf qgj

nkfj N. }kqg slkqklf rjoqly ˂ ˂ ˂y wk {e ud

&

Bylh qgj bkmzyj. }j g`rj

@I LI L@ i `

&

Gjfoj qgj yjpzkyja nkfj s`j qgylzmg @

`fa k s`y`nnjn ql @I k&j&i `

. `fa kq rjoqly

jpz`qklf. qgz. k 'y `+ 8 'i `+•'1+ 

u

w

L {

S

@ y

 

`

 

i

 

I

ly. y ` 'i `+

. • ':+

O`yqjk`f Blyh5Bylh '1+. }j g`rj

0 0 0 9 0 9 0 9 0˂ ˂ ˂ ˂ ˂ ˂'w w +k '{ { +e 'u u +d 'w w +k '{ { +e 'u u +d &

Olhs`ykfm qgj oljbbkokjfq lb ˂ ˂ ˂k. e d`fa . }j liq`kf

'w w0+ 8 'w9 w0+. { {0 8 '{9 {0+. u u0 8 'u9 u0+

ly 0 0 0

9 0 9 0 9 0

w w { { u u

w w { { u u& • '2+ 

Qgjj `yj qgj O`yqjk`f jpz`qklf lb qgj nkfj s`kfm qgylzmg qgj slkfq 'w0. {0. u0+ `fa'w9. {9. u9+&

Olnnkfj`ykq{ lb qgyjj slkfq

Njq @. I. O ij qgyjj mkrjf slkfq }kqg slkqklf rjoqly `. i `fa o

yjsjoqkrjn{& Qgj

jpz`qklf lb qgj nkfj qgylzmg @ `fa I k

y ` 'i `+ '0 +` i y 3ly

&

Kb @. I. O `yj olnnkfj`y. qgjf O nkj lf @I

'0 +` i o 3

& • '=+ 

Qgk yjsyjjfq ` yjn`qklf ijq}jjf qgj slkqklf rjoqly lb qgj slkfq @. I. O. }gkog `yj

olnnkfj`y& ]j flqj qg`q qgj `nmjiy`ko zh lb qgj oljbbkokjfq lb `. i. o

k 0 $ 0 8

3&Njq z fl} `zhj qg`q `f{ qgyjj rjoqly z. r. }

`qkb{ qgj yjn`qklf

0 9 ?d z d r d } 3

}kqg d0 $ d9 $ d? 8 3&

Akrkakfm i{ d? ' 3+. }j mjq

0 9

? ?

d dz r } 3

d d

}kqg 0 9

? ?

d d0 3

d d 

8/4/2019 Wikimama Class 11 ch 12 3-D

http://slidepdf.com/reader/full/wikimama-class-11-ch-12-3-d 3/3

?

l qg`q 0 0

? ?

d dz 0 r } 3

d d

 

0 0

? ?

d d} z 0 r z '0 +r

d d

. }gjyj 8 0

?

d

d&

Gjfoj O }kqg slkqklf rjoqly o

k olnnkfj`y }kqg @ `fa I& ]j olfonzaj qg`q qgyjj slkfq`yj olnnkfj`y kb qgjyj jwkq ` nkfj`y yjn`qklf ijq}jjf qgjh. zog qg`q qgj zh lb qgj

oljbbkokjfq kf kq k ujyl&_glyqjq akq`foj ijq}jjf q}l nkfj 

Olfkajy q}l nkfj N0 `fa N9 kf s`oj&

qgjf SP 8 @I ol 8'o a+ 'i `+

~ i ` ~~ o a ~ ~ i ` ~

'o a+ 'i `+

~ o a ~

 

Flqj 5 

0& Qgj nkfjs N0 `fa N9  }knn kfqjysjoq kb `fa lfn{ kb 

qgj sglyqjsq aksq`foj ijq}jjf qgjh ks ujyl k&j& SP 8 3 

ly  o a i ` 3

&

ly  i ` o a 3

 S@'`+

 

I'i+

 P

N9

N9

9& Kb qgj nkfj N0 `fa N9 `yj yjsjoqkrjn{

0 0 0

0 0 0

w w { { u u

n h f`fa 9 9 9

9 9 9

w w { { u u

n h f.

qgj olfakqklf `ilrj bly kfqjyjoqkfm nkfj ijolhj

0 9 0 9 0 9

0 0 0

9 9 9

w w { { u u

n h f 3

n h f

&

?& Qgj nkfj N0 `fa N9 `yj dj} kb

0 9 0 9 0 9

0 0 0

9 9 9

w w { { u u

n h f 3

n h f

&

`fa qgjf qgj glyqjq akq`foj ijq}jjf N0 `fa N9 k

9 0 9 0 9 0

0 0 0

9 9 9

9 9 90 9 09 0 9 0 9 0 9 9 0

w w { { u u

n h fn h f

'n h h n + 'h f f h + 'n f n f +&

1& Kb `f{ qy`kmgq nkfj k mkrjf kf mjfjy`n blyh qgjf kq o`f ij qy`fblyhja kfql

{hhjqyko`n blyh `fa }j o`f sylojja bzyqgjy&