Amaliy mashg’ulot uchun misollar

TEKISLIK VA TO’G’RI CHIZIQ.

1. to’g’ri chiziq bilan 12x + 3y - 4z + 4 = 0 tekislik orasidagi burchakni hisoblang.

2. to’g’ri chiziq bilan 2x - 3y - 2z + 5 = 0 tekislik orasidagi burchakni hisoblang.

3. M(2,-3,4) nuqtadan to’g’ri chiziqqa perpendikulyar holda o’tuvchi tekislik tenglamasini tuzing.

4. N(-1,2,-3) nuqtadan to’g’ri chiziqqa perpendikulyar holda o’tuvchi tekislik tenglamasini tuzing.

5. Quyida berilgan to’g’ri chiziq bilan tekislik kesishish nuqtasini toping.

1) , x + 2y - 3z – 4 = 0.

2) , 2x + 3y + z - 1 = 0.

3) , x + 2y - 2z + 6 = 0.

6. M(1,3,2) nuqtadan o’tib, x - 2y + 2z – 3 = 0 tekislikka perpendikulyar to’g’ri chiziq tenglamasini tuzing.

7. M(-1,1,-2) nuqtadan o’tib, 4x - 5y – z – 3 = 0 tekislikka perpendikulyar ravishda o’tuvchi to’g’ri chiziq tenglamasini tuzing.

8. Quyida berilgan to’g’ri chiziqning tekislikda yotishini tekshiring.

1) .

2) .

3) .

9. m ning qanday qiymatida to’g’ri chiziq

x - 3y + 6z + 7 = 0 tekislikka parallel bo’ladi?

10. C ning qanday qiymatida to’g’ri chiziq

2x – y + Cz - 2=0 tekislikka parallel bo’ladi?

11. Ushbu to’g’ri chiziqqa nisbatan P(4;3;10) nuqtaga simmetrik bo’lgan nuqtani toping.

12. P(7;9;7) nuqtadan to’g’ri chiziqqacha bo’lgan masofani toping.

13. P(1,-1,-2) nuqtadan to’g’ri chiziqqacha bo’lgan masofani toping.

14. Quyidagi ikki parallel to’g’ri chiziq orasidagi masofani toping. va