Amaliy mashg’ulot uchun misollar

FAZODA TO’G’RI CHIZIQ

1. Ozod had D ning qanday qiymatlarida quyidagi to’g’ri chiziq: 1) Ox 2) Oy 3) Oz o’qini kesadi.

2. 6x - 17y + 12z – 13 = 0 tekislik bilan koordinatalar tekisligining kesishishidan hosil bo’lgan to’g’ri chiziq tenglamalarini tuzing.

3. M₁(3,5,0) nuqtadan o’tgan: 1) a = (8, -3, 2) vektorga;

2) to’g’ri chiziqqa; 3) Ox o’qiga; 4) Oy o’qiga; 5) Oz o’qiga parallel bo’lgan to’g’ri chiziq tenglamasini tuzing.

4. Quyida berilgan ikki nuqta orqali o’tgan to’g’ri chiziq tenglamasini tuzing:

1) (2; -2; 3), (3; 4; -1); 2) (-8;-1;6), (4;0;-5);

3) (6; -2;5), (8;-3;4); 4) (7;-2;-4), (5;2;6).
5. Quyida berilgan to’g’ri chiziqlarning kanonik tenglamasini tuzing.

1) 2x + 2y + 3z – 4 = 0, x + 2y - 3z + 4 = 0;

2) 5x + y + z = 0, 2x + 3y - 2z + 5 = 0;

3) 2x – y + 3z – 2 = 0, 3x + y - 4z – 8 = 0.

6. Quyida berilgan to’g’ri chiziqlarning parametrik tenglamasini tuzing.

1) 2x + 3 y – z – 4 = 0, 3x - 5y + 2z – 1 = 0;

2) x + 2y – z – 6 = 0, 2x – y + z + 1 = 0.
7. Quyida berilgan to’g’ri chiziqlarning parallelligini isbotlang.

1) va

2) va

3) va

8. Quyidagi berilgan to’g’ri chiziqlarning perpendikulyarligini isbotlang.

1) va

2) va

3) va
9. Quyida berilgan ikki to’g’ri chiziq orasidagi o’tkir burchakni toping.

1) va .

2) va .

3) va

10 Uchburchakning A(3,6,-7), B(-5,2,3) va C(4,-7,-2) uchlari berilgan. Uning S uchidan tushirilgan medianasining parametrik tenglamasini tuzing.