sirt tenglamasi. fazoda tekislik va to’гri chiziq tenglamalari

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1662970029.doc z y x , , ( ) 0 , , = z y x f z y x , , z y x , , 0 0 0 , , z z y y x x = = = 0 0 0 , , z y x ( ) 0 0 0 , , z y x m ( ) z y x m , , ( ) c b a c , , r ( ) ( ) ( ) , 2 2 2 r c z b y a x = - + - + - ( ) ( ) ( ) . 2 2 2 2 r c z b y a x = - + - + - . 2 2 2 2 r z y x = + + 0 = + + + d cz by ax 0 2 2 2 2 2 …

0 z n sirt tenglamasi sirt tenglamasi. fazoda tekislik va to’гri chiziq tenglamalari reja: 1. umumiy tushunchalar 2. fazodagi tekislik tenglamalari. 3. tekislikning kesmalardagi tenglamasi. 4. tekislikning normal tenglamasi. 1. umumiy tushunchalar. faraz qilaylik, - iхtiyoriy o’zgaruvchi miqdorlar bo’lsin. agar (1) tenglik larning faqat ayrim qiymatlaridagina o’rinli bo’lsa, u holda (1) ni larga nisbatan tenglama deb ataymiz. uchta son (1) tenglamani qanoatlantiradi deymiz, agar (1) dagi noma’lumlar o’rniga shu sonlarni qo’yganda tenglik ayniyatga aylansa. (1) tenglamani qanoatlantiradigan хar bir sonlar uchligiga fazoning nuqtasini mos qo’yamiz. bunday nuqtalarning geometrik o’rnini sirt deb ataymiz, (1) ni esa shu sirtning tenglamasi deymiz. agar sirt tenglamasi berilgan bo’lib, biror nuqtaning shu sirtda yotish yoki yotmasligini tekshirish talab qilingan bo’lsa, u holda berilgan nuqtaning koordinatalarini tenglamaning noma’lumlari o’rniga qo’yish kifoya. analitik geometriyaning vazifasi qaralayotgan sirtni uning tenglamasi yordamida o’rganishdir. sirtning iхtiyoriy nuqtasi uning ¢zgaruvchi nuqtasi deb ataladi. misol sifatida sferaning tenglamasini tuzaylik. sferaning ta’rifiga ko’ra, …

tasi bo’lsin. bu nuqta tekisligida yotishi uchun vektor ga perpendikulyar bo’lishi shart, ya’ni embed equation.3 embed equation.3 , . vektorlarning perpendikulyarlik shartidan embed equation.3 yoki (4) kelib chiqadi . agar nuqta tekisligida yotmasa, (4) o’rinli bo’lmaydi, shu sababli (4) tenglik nuqtaning o’rnini to’la aniqlaydi. agar (4) dagi qavslarni ochib va deb belgilasak, hosil bo’ladi. teorema isbot bo’ldi. tekislikka perpendikulyar bo’lgan nol bo’lmagan хar qanday vektor tekislikka normal vektor deb, shu sababli, (4) tenglama normal vektori bo’lib , nuqtadan o’tgan tekislik tenglamasi deb ataladi. teorema 2. dekart koordinatalar sistemasida хar qanday 1-tartibli tenglama tekislikni aniqlaydi. isboti. biror dekart koordinatalar sistemasida (3) tenglama berilgan bo’lsin. faraz qilaylik, lar shu tenglamaning biror echimi bo’lsin, ya’ni (3) ni qanoatlantiruvchi sonlar bo’lsin. u holda (5) bo’ladi. (3) dan (5) ni ayirsak hosil bo’ladi. ma’lumki, bu tenglama normal vektori bo’lib , nuqtadan o’tgan tekislik tenglamasidir. (4) tenglama (3) ga ekvivalent bo’lgani uchun (3) ham tekislikning tenglamasi …

tekislikning kesmalardagi tenglamasi. ma’lumki, koeffitsientlar bir vaqtda nolga teng bo’lmaydi. (3) tenglamada bu koeffitsientlarning ayrimlari nolga teng bo’lgan bir necha hususiy hollarni ko’rib chiqaylik. 1) ; tenglama ko’rinishga keladi. bu tenglamani sonlar qanoatlantiradi,ya’ni tekislik koordinatalar boshidan o’tadi. 2) s=0 ; tenglama ko’rinishda bo’ladi. bu tekislikning normal vektori o’qiga perpendikulyar , demak, tekislikni o’zi shu o’qga parallel o’tadi. 3) ; bunda ga ega bo’lamiz. uning normal vektori va o’qlariga perpendikulyar , u holda tekislik tekisligiga parallel o’tadi. o’ususan, agar bo’lsa, hosil bo’lib, bu tekislik koordinatalar tekisligi bilan ustma-ust tushushiga ishonch hosil qilamiz. yuqoridagidek fikr yuritib, tenglama o’qiga parallel tekislikni, tenglama o’qiga parallel tekislikni aniqlashiga ishonch hosil qilamiz. bularning hususiy holi sifatida, tenglama koordinatalar tekisligining, esa tekisligining tenglamasi ekanligini ko’ramiz. 4) koeffitsientlarning birortasi ham nolga teng bo’lmasin. u holda ozod hadni tenglikning o’ng tomoniga o’tkazib, tenglamani ga bo’lib yuboramiz: yoki agar belgilashlar kiritsak, (6) hosil bo’ladi. (6) tenglamani tekislikning kesmalardagi tenglamasi deb …

d ning ishorasiga teskari qilib olinsa kifoya. (3) tenglama ifoda yordamida normal ko’rinishga keltirilgani uchun 1/ ni normallovchi ko’paytuvchi deb atashadi. 1 4 _1025921103.unknown _1025925908.unknown _1025927738.unknown _1025947337.unknown _1025948641.unknown _1124622419.unknown _1124622482.unknown _1025948845.unknown _1025950161.unknown _1025964323.unknown _1077284754.doc _1025950243.unknown _1025948988.unknown _1025948772.unknown _1025947887.unknown _1025948159.unknown _1025948376.unknown _1025948006.unknown _1025947666.unknown _1025947757.unknown _1025947536.unknown _1025928363.unknown _1025946579.unknown _1025946935.unknown _1025947306.unknown _1025946701.unknown _1025928633.unknown _1025946496.unknown _1025928510.unknown _1025927995.unknown _1025928218.unknown _1025928292.unknown _1025928114.unknown _1025927914.unknown _1025927978.unknown _1025927881.unknown _1025926816.unknown _1025927293.unknown _1025927675.unknown _1025927711.unknown _1025927605.unknown _1025927028.unknown _1025927245.unknown _1025927058.unknown _1025927143.unknown _1025926936.unknown _1025926445.unknown _1025926593.unknown _1025926695.unknown _1025926530.unknown _1025926160.unknown _1025926244.unknown _1025926108.unknown _1025924007.unknown _1025924973.unknown _1025925408.unknown _1025925546.unknown _1025925637.unknown _1025925485.unknown _1025925027.unknown _1025925350.unknown _1025924997.unknown _1025924575.unknown _1025924843.unknown _1025924886.unknown _1025924640.unknown _1025924245.unknown _1025924292.unknown _1025924089.unknown _1025921620.unknown _1025923220.unknown _1025923814.unknown _1025923885.unknown _1025923634.unknown _1025922264.unknown _1025922653.unknown _1025921772.unknown _1025921856.unknown _1025921375.unknown _1025921415.unknown _1025921502.unknown _1025921259.unknown _1025903468.unknown _1025904298.unknown _1025920854.unknown _1025920945.unknown _1025903631.unknown _1025903767.unknown _1025904162.unknown _1025903514.unknown _1025900680.unknown _1025903186.unknown

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1662970029.doc z y x , , ( ) 0 , , = z y x f z y x , , z y x , , 0 0 0 , , z z y y x x = = = 0 0 0 , , z y x ( ) 0 0 0 , , z y x m ( ) z y x m , , ( ) c b a c , , r ( ) ( ) ( ) , 2 2 2 r c z b y a x = - + - + - ( ) ( ) ( ) . 2 2 2 2 r c z b y a x = - + …

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