tekislik tenglamalari

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13-amaliy mashg’ulot:tekislik tenglamalari,ularning xususiy hollari.tekislikni yasash. tekisliklar orasidagi burchak. namunaviy misollar yechish: 1-misol. tenglik tenglamasini normal tenglamaga keltiring. yechish: normal ko’rinishga keltirish uchun normallovchi ko’paytuvchi ni topamiz: chunki, , demak, berilgan tenglamani barcha hadlarini ga ko’paytirib, normal tenglamaga keltiramiz. bu yerda , , , tekislikka o’tkazilgan normal vektorning yo’naltiruvchi kosinuslari. 2-misol. tekislikning kesmalar bo’yicha tenglamasini yozing. yechish: berilgan tekislik tenglamasini har bir hadini 8 ga bo’lib yuboramiz: va ko’rinishga keltiramiz. demak, tekislik koordinata o’qlaridan kabi kesmalar ajratar ekan. 0 у х z -2 7-rasm 3-misol. m(1, 2, 1) nuqtadan nuqtadan tekislikkacha bo’lgan masofani toping. yechish: berilgan tekislik tenglamasini normal ko’rinishga keltiramiz: va nuqtadan tekislikkacha bo’lgan masofani topish uchun tekislikning normal tenglamasidagi x, y, z lar o’rniga nuqtaning koordinatalarini qo’llaymiz: 4-misol. -nuqtalar berilgan. nuqtadan o’tib, vektorga perpendikulyar bo’lgan tekislik tenglamasini tuzing. yechish: bu masalani yechish uchun vektorni tuzib olamiz va ekanligidan va berilgan nuqtadan o’tuvchi tekislik tenglamasidan foydalanib, yoki tekislik tenglamasini …

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da bo‘lgan uchburchakning medianasining uzunligini toping. 6. va nuqtalarga parallel yo’nalgan va kuchlar qo‘yilgan. ularning teng ta’sir etuvchisi qo‘yilgan nuqtani toping. va . ko‘rsatma: fizikadan ma’lumki parallel kuchlarni qo‘shganda va yelkalar unga qo‘yilgan kuchlarga teskari proporsianaldir, ya’ni bo‘ladi. 7. va nuqtalarga va parallel kuchlar qo‘yilgan. , bo‘lsa teng ta’sir etuvchi kuchning qo‘yilgan nuqtasini toping. 8. nuqtadan o‘tib, vektorga perpendikulyar bo‘lgan tekislik tenglamasini yozing. 9. nuqtadan o‘tib, ordinat o‘qidan , aplikata o‘qidan kesma ajratib o‘tgan tekislik tenglamasini yozing. 10. o‘qiga parallel va , nuqtalardan o‘tuvchi tekislik tenglamasini yozing. 11. tenglik tenglamasini normal tenglamaga keltiring. 12. tekislikning kesmalar bo’yicha tenglamasini yozing. 13. m(3, 2, 1) nuqtadan nuqtadan tekislikkacha bo’lgan masofani toping. 14. -nuqtalar berilgan. nuqtadan o’tib, vektorga perpendikulyar bo’lgan tekislik tenglamasini tuzing. 15. nuqtalardan o’tib, tekislikka perpendikulyar tekislik tenglamasi tuzilsin. image4.wmf oleobject49.bin image47.wmf oleobject50.bin image48.wmf oleobject51.bin image49.wmf oleobject52.bin image50.wmf oleobject53.bin image51.wmf oleobject4.bin oleobject54.bin image52.wmf oleobject55.bin image53.wmf oleobject56.bin image54.wmf oleobject57.bin image55.wmf oleobject58.bin image56.wmf …

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image77.wmf oleobject80.bin image78.wmf oleobject81.bin image79.wmf oleobject82.bin image80.wmf oleobject83.bin image81.wmf oleobject7.bin oleobject84.bin image82.wmf oleobject85.bin image83.wmf oleobject86.bin image84.wmf oleobject87.bin image85.wmf oleobject88.bin image86.wmf image8.wmf oleobject89.bin image87.wmf oleobject90.bin image88.wmf oleobject91.bin image89.wmf oleobject92.bin image90.wmf oleobject93.bin image91.wmf oleobject8.bin oleobject94.bin image92.wmf oleobject95.bin image93.wmf oleobject96.bin image94.wmf oleobject97.bin oleobject98.bin oleobject99.bin image95.wmf image9.wmf oleobject100.bin oleobject101.bin oleobject9.bin image10.wmf oleobject10.bin image11.wmf oleobject11.bin image12.wmf oleobject12.bin image13.wmf oleobject13.bin image14.wmf oleobject14.bin image15.wmf oleobject15.bin image16.wmf oleobject16.bin image17.wmf oleobject17.bin image18.wmf oleobject18.bin image1.wmf image19.wmf oleobject19.bin image20.wmf oleobject20.bin image21.wmf oleobject21.bin image200.wmf oleobject22.bin image210.wmf oleobject23.bin oleobject1.bin image22.wmf oleobject24.bin image23.wmf oleobject25.bin image24.wmf oleobject26.bin image25.wmf oleobject27.bin image26.wmf oleobject28.bin image2.wmf image27.wmf oleobject29.bin image28.wmf oleobject30.bin image29.wmf oleobject31.bin image30.wmf oleobject32.bin image31.wmf oleobject33.bin oleobject2.bin image32.wmf oleobject34.bin image33.wmf oleobject35.bin image34.wmf oleobject36.bin image35.wmf oleobject37.bin image36.wmf oleobject38.bin image3.wmf image37.wmf oleobject39.bin image38.wmf oleobject40.bin image39.wmf oleobject41.bin image40.wmf oleobject42.bin oleobject43.bin image41.wmf oleobject3.bin oleobject44.bin image42.wmf oleobject45.bin image43.wmf oleobject46.bin image44.wmf oleobject47.bin image45.wmf oleobject48.bin image46.wmf 300 d =- 0 7 9 6 8 7 1 7 5 6 10 7 5 7 6 7 = …

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13-amaliy mashg’ulot:tekislik tenglamalari,ularning xususiy hollari.tekislikni yasash. tekisliklar orasidagi burchak. namunaviy misollar yechish: 1-misol. tenglik tenglamasini normal tenglamaga keltiring. yechish: normal ko’rinishga keltirish uchun normallovchi ko’paytuvchi ni topamiz: chunki, , demak, berilgan tenglamani barcha hadlarini ga ko’paytirib, normal tenglamaga keltiramiz. bu yerda , , , tekislikka o’tkazilgan normal vektorning yo’naltiruvchi kosinuslari. 2-misol. tekislikning kesmalar bo’yicha tenglamasini yozing. yechish: berilgan tekislik tenglamasini har bir hadini 8 ga bo’lib yuboramiz: va ko’rinishga keltiramiz. demak, tekislik koordinata o’qlaridan kabi kesmalar ajratar ekan. 0 у х z -2 7-rasm 3-misol. m(1, 2, 1) nuqtadan nuqtadan tekislikkacha bo’lgan masofani toping. ye...

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