1. Vektorlar haqida tushincha. 1-ta’rif. O’zining son qiymati va yo’nalishi bilan aniqlanadigan miqdorlar vektorlar deb ataladi. 2-ta’rif

Mustaqil yechish uchun misol va masalalar
1. Ushbu A(3;2;-2), B(-2;0;0), C(-3;1;0), D(-4;-2;2,5) nuqtalar berilgan. Bu nuqtalardan qaysilari 2x - 3y + 2z + 4 = 0 tekislikka tegishli bo’lishini ko’rsating. 2. 1) M(-3;0;2) nuqtadan o’tuvchi va =(1,3,4) vektorga perpendikulyar tekislikning tenglamasini tuzing.
2) M(6;4;5) nuqtadan o’tuvchi va =(-1,-3,2) vektorga perpendikulyar tekislikning tenglamasini tuzing.
3) A(4;-2;3) va B(1;4;2) nuqtalar berilgan. A nuqtadan o’tuvchi va AB vektorga perpendikulyar bo’lgan tekislikning tenglamasini tuzing.
3. 1) Ox o’qdan va M(3;2;4) nuqtadan o’tuvchi;
2) Oy o’qdan va M(-2;-3;-4) nuqtadan o’tuvchi;
3) Oz o’qdan va M(1;1;1) nuqtadan o’tuvchi tekislik tenglamasini tuzing.
4. M(2;-1;3) nuqtadan o’tuvchi va = (3,0,-1) hamda = (-3,2,2) vektorlarga
parallel ravishda o’tuvchi tekislikning tenglamasini tuzing.
5. 1) M(-2;3;4) nuqtadan o’tuvchi va x + 2y - 3z + 4=0 tekislikka parallel bo’lgan tekislikning tenglamasini tuzing.
2) M₁(-2; -3; 1) va M₂(1; 4; -2) nuqtalardan o’tuvchi va 2x - 3y – z + 4 = 0 tekislikka perpendikulyar bo’lgan tekislikning tenglamasini tuzing.
6. Quyidagi tekisliklarning koordinata o’qlaridan ajratgan kesmalarini hisoblang:
1) 4x - 3y – z + 12=0 ; 2) 5x + y - 4z - 20=0 ;3) x - 8z – 16 = 0 ;4) y – 7 = 0. 7. Quyidagi berilgan tekislik tenglamalarini normal shaklga keltiring.
1) 2x - 9y + 6z - 22=0; 2)
3) 4x + 3y + 12z + 6 = 0.
8. 1) A(2;3;4) nuqtadan 4x + 3y + 12z – 5 = 0 tekislikkacha
2) B(3; 1; -1) nuqtadan 3x – y + 2z + 1 = 0 tekislikkacha
3) C(2; 0; -1/2) nuqtadan 4x - 4y + 2z + 17 = 0 tekislikkacha bo’lgan masofani toping.
9. Quyida berilgan tekisliklar orasidagi o’tkir burchaklarni toping.
1) 2x - 3y + 4z – 1 = 0 va 3x – 4 y – z + 3 = 0 ;
2) x – y + z + 1 = 0 va 2x + 3y + z – 3 = 0 ;
3) 4x – 5 y + 3z – 1 = 0 va x - 4y – z + 9 = 0.
10. Quyidagi 1) 11x - 2y - 10z + 75 = 0 va 11x - 2y - 10z – 45 = 0;
2) 2x - 3y + 6z + 28 = 0 va 2x - 3y + 6z – 14 = 0
parallel tekisliklar orasidagi masofani toping.
11. Quyida berilgan uchta tekislikning kesishish nuqtasini toping.
1) 3x - 5y + 3z – 1 = 0, x + 2y + z – 4 = 0, 2x + 7y – z - 8 = 0;
2) 2x - 4y + 9z - 28 =0, 7x + 9y - 9z – 5 = 0, 7x + 3y - 6z + 1 = 0;
3) 2x + y – 5 = 0, x + 3z – 16 = 0, 5y – z – 10 = 0.
12. Kubning ikkita yog’i 2x – 2 y + z – 1 = 0 va 2x - 2y + z + 5 = 0 tekisliklarda yotadi. Bu kubning hajmini hisoblang.
13. M₁(3; 4 ; -5) nuqtadan o’tgan, = {3, 1, -1} va = {1, -2, 1} vektorlarga parallel bo’lgan tekislik tenglamasini tuzing.
14. M₁(3; -1; 2), M₂(4; -1; -1) va M₃(2; 0; 2) nuqtalar orqali o’tgan tekislik tenglamasini tuzing.
15. M₁(2; -1; 3) va M₂(3; 1; 2) nuqtalar orqali o’tgan = {3, -1, 4} vektorga parallel bo’lgan tekislik tenglamasini tuzing.