I. Burchaklar

VIII. Tekislikda Vektorlar

1. (0;-2) va (-3;4) vektorlar berilgan. vektorning koordinatalarini toping. (96–1–42)
A)(0;8) B)(3;-6) C)(6;-8) D)(6;-14) E)(-6;-8)
2. (2;-3) va (-2;-3) vektorlar berilgan. vektorning koordinatalarini toping. (96–9–94)
A)(6;3) B)(-3;6) C)(-2;-9) D)(2;-3) E)(0;3)
3. (-3;1) va (5;-6) vektorlar berilgan. vektorning koordinatalarini toping. (96–10–44)
A)(14;-9) B)(4;-3) C)(14;-3) D)(9;3) E)(-5;6)
4. (4;1) va (-2;2) vektorlar berilgan. Agar bo`lsa, vektorning koordinatalarini toping. (97–1–35)
A)(-2;5) B)(2;-5) C)(-10;4) D)(10;-5) E)(-6;4)
5. (-5;0) va (-1;4) vektorlar berilgan. Agar bo`lsa, vektorning koordinatalarini toping. (97–6–35)
A)(-2;2) B)(-3;2) C)(1;0) D)(2;2) E)(3;-2)
6. (0;-4) va (-2;2) vektorlar berilgan. Agar bo`lsa, vektorning koordinatalarini toping. (97–11–35)
A) (2;-14) B) (3;-6) C) (-2;10)
D) (-2;-10) E) (2;-10)
7. Agar va bo`lsa, vektorning koordinatalarini toping. (98–1–47)
A)(-4;12) B)(-4;0) C)(4;0) D)(2;-6) E)(-2;4)
8. To`rtburchakning M(2;-4); N(-4;0) va P(2;-2) uchlari berilgan. Agar bo`lsa, Q uchining koordintalarini toping. (98–2–53)
A)(-7;1) B)(3,5;-3) C)(-7;-1) D)(7;1) E)(6;-1)
9. Agar va bo`lsa, vektorning koordinatalarini toping. (98–8–47)
A)(10;-3) B)(-6;4) C)(-2;3) D)(4;-4) E)(-10;3)
10. (8;6) vektor va vektrolarga yoyilgan. Agar , (10;-3) va (-2;1) bo`lsa, μλ ning qiymatini aniqlang. (00–1–54)
A) 120 B) 115 C) 110 D) 100 E) 105
11. vektor berilgan. 3· vektorning modulini toping. (96–3–40)
A) 4,5 B) 3,5 C) 5 D) 5,5 E) 2,5
12. vektor berilgan. 4· vektorning modulini toping. (96–11–41)
A) 13 B) 17 C) 18 D) 15 E) 12
13. vektor berilgan. 2· vektorning modulini toping. (96–12–42)
A) 5 B) 4 C) 7 D) E)
14. Agar va o`zaro perpendikulyar birlik vektorlar bo`lsa, vektorning uzunligini toping. (97–1–37)

15. (-6;8) vektor berilgan bo`lib, bo`lsa, λ ni toping. (99–1–36)

16. (5;1) va (-2;3) vektorlar berilgan. ni hisoblang. (97–5–29)
A) 5 B) 3 C) 4 D) 2 E) 1
17. (7;3) va (5;2) vektorlar berilgan. ni hisoblang. (97–9–29)
A) 19 B) 5 C) 8 D) 13 E) 12
18. (2,5;-1) va (-2;-2) bo`lsa, vektorning uzunligini toping. (98–9–52)
A) 12 B) 8 C) 14 D) 6 E) 10
19. (3;2) va (0;-1) vektorlar berilgan. vektorning modulini toping. (99–6–19)
A) 10 B) 6 C) 8 D) 3 E) 5
20. A(2;4), B(3;6) va C(6;14) nuqtalar berilgan. ni hisoblang. (99–8–58)
A) 13 B) 12 C) 10 D) 14 E)
21. Agar bo`lsa, ning qiymatini toping. (00–6–45)

22. va birlik vektorlar orasidagi burchak 30⁰. ni toping. (98–11–86)

23. va vektorlar 120⁰ li burchak hosil qiladi. Agar va bo`lsa, ning qiymati qanchaga teng bo`ladi? (98–12–103)
A) 2 B) 8 C) 7 D) 6 E) 10
24. va vektorlar 120⁰ li burchak tashkil qiladi hamda va bo`lsa, ning qiymatini toping. (99–4–46)

25. , bo`lsa, vektorlar ga teng burchak tashkil qiladi. vektorning uzunligini toping. (99–3–40)
A) B) 12 C) 17 D) E) 13
26. va birlik vektorlar orasidagi burchak 60⁰. ni toping. (98–6–37)

27. n(n>0) ning qanday qiymatida (2n;3) va (6;n) vektorlar kollenear bo`ladi? (99–6–20)
A) 1 B) 3 C) 2 D) 4 E) 6
28. (2;-4), (1;2), (1;-2) va (-2;-4) vektorlarlardan qaysilari kollenear vektorlar?
(99–1–48)
A) , ; , B) , C) , D) , E) kollenearlari yo`q
29. (3;4) vektor yo`nalishidagi birlik vektorni toping. (00–10–59)

30. va nokollenear vektorlarlar berilgan. bo`lsa, ( + ) bilan ( – ) qanday burchak tashkil etadi? (96–3–43)
A) 30⁰ B) 45⁰ C) 90⁰ D) 60⁰ E) 75⁰
31. (2;5) va (-7;-3) vektorlar orasidagi burchakni toping. (96–7–40)
A) 150⁰ B) 135⁰ C) 120⁰ D) 60⁰ E) 45⁰
32. va nokollenear vektorlarlar berilgan. bo`lsa, ( + ) bilan ( – ) qanday burchak tashkil etadi? (96–11–44)
A) 30⁰ B) 45⁰ C) 60⁰ D) 75⁰ E) 90⁰
33. va nokollenear vektorlarlar berilgan. bo`lsa, ( + ) bilan ( – ) qanday burchak tashkil etadi? (96–3–43) (96–12–46)
A) 45⁰ B) 90⁰ C) 75⁰ D) 60⁰ E) 30⁰
34. (5;-3) va (4;1) vektorlar orasidagi burchakni toping. (97–3–40)
A) 135⁰ B) 120⁰ C) 60⁰ D) 45⁰ E) 30⁰
35. (7;3) va (-2;5) vektorlar orasidagi burchakni toping. (97–7–40)
A) 30⁰ B) 45⁰ C) 60⁰ D) 135⁰ E) 150⁰
36. (1;0) va (1;-1) vektorlar orasidagi burchakni toping. (97–10–40)
A) 30⁰ B) 45⁰ C) 60⁰ D) 90⁰ E) 135⁰
37. va vektorlar orasidagi burchakni toping. (98–5–37)

38. Agar va bo`lsa, vektorlar orasidagi burchakni toping. (00–7–44)
A) 120⁰ B) 130⁰ C) 128⁰ D) 150⁰ E) 135⁰
39. (1;2) va (2;1) vektorlar orasidagi burchak sinusini toping. (99–7–36)

40. Uchlari A(-1;5), B(3;1) va C(-1;-3) nuqtalarda bo`lgan uchburchakning A va B burchaklarini toping. (96–12–47)
A) 60⁰; 30⁰ B) 90⁰; 45⁰ C) 30⁰; 45⁰
D) 45⁰;45⁰ E) 45⁰; 90⁰
41. Uchlari A(1;1), B(-2;3) va C(-1;-2) nuqtalarda bo`lgan uchburchakning A va B burchaklarini toping. (96–3–44)
A) 60⁰; 30⁰ B) 90⁰; 45⁰ C) 30⁰; 90⁰
D) 45⁰; 90⁰ E) 45⁰;45⁰
42. Uchlari A(-2;3), B(-1;-2) va C(1;1) nuqtalarda bo`lgan uchburchakning A va C burchaklarini toping. (96–11–45)
A) 45⁰; 90⁰ B) 90⁰; 45⁰ C) 30⁰; 90⁰
D) 45⁰; 45⁰ E) 90⁰; 30⁰
43. Agar M(1;1), N(2;3) va K(-1;2) bo`lsa, MNK uchburchakning eng katta burchagini toping.
(97–1–36)
A) 75⁰ B) 90⁰ C) 120⁰ D) 135⁰ E) 105⁰

44. Uchlari A(0;0), B(3;4) va C(8;6) nuqtalarda bo`lgan uchburchakning A burchagini toping.

(98–10–90)
A) arccos 0,96 B) arccos 0,92 C) D)arccos 0,9 E) arccos0,98
45. Uchlari A(1;2), B(1;4) va C(3;2) nuqtalarda bo`lgan uchburchakning katta burchagini toping. (97–11–36)
A) 110⁰ B) 90⁰ C)120⁰ D) 135⁰ E) 150⁰
46. Uchlari A(0;0), B(4;3) va C(6;8) nuqtalarda bo`lgan uchburchakning A burchagini toping. (98–10–90)
A) arccos 0,9 B) C)
D) arccos 0,96 E) arccos 0,94
47. Uchlari O(0;0), M(1;1), P(0;2) va K(-1;1) nuqtalarda bo`lgan, OMPK to`rtburchak diagonallari orasidagi burchakni toping.
(97–6–36)
A) 90⁰ B) 30⁰ C) 60⁰ D) 45⁰ E) 75⁰
48. vektorlar 45⁰ li burchak tashkil qiladi va . Shu vektorlarga qurilgan uchburchakning yuzini toping. (98–1–46)
A) 4 B) C) D) 2 E) 8
49. Agar vektorlar 30⁰ li burchak tashkil etsa va bo`lsa, ularga qurilgan parallelogrammning yuzini hisoblang. (98–8–46)
A) 2 B) C) 1 D) E) 1,5
50. Agar bo`lsa, tengsizlik x ning qanday qiymatlarida o`rinli bo`ladi? (98–8–46)
A)(-1;3) B)(0;2) C)(1;2) D)(-3;-1) E)(-∞;-1)
51. Agar vektorlar perpendikulyar bo`lsa, birlik vektorlar orasidagi burchakni toping. (97–6–37)
A) 30⁰ B) 45⁰ C) 60⁰ D) 120⁰ E) 90⁰
52. Agar vektorlar 120⁰ li burchak tashkil etuvchi birlik vektorlar bo`lsa, va vektorlar orasidagi burchakni toping. (97–11–37)
A) 120⁰ B) 90⁰ C) 135⁰ D) 150⁰ E) 60⁰
53. birlik vektorlar berilgan. Agar bo`lib, vektorlar orasidagi burchak 60<sup>0</sup> ga teng bo`lsa, skalyar ko`paytmaning qiymatini toping. (99–9–42)
A) 2 B) 2,2 C) 2,4 D) 2,5 E) 2,1
54. . λ ning qanday qiymatida bo`ladi? (96–3–99)
A) 1 B) 2 C) 3 D) 1,5 E) 2,5
55. . λ ning qanday qiymatida bo`ladi? (96–9–39)

56. . λ ning qanday qiymatida bo`ladi? (96–12–101)
A) -2 B) -1,5 C) D) -2,5 E) -0,5
57. . λ ning qanday qiymatida bo`ladi? (96–13–41)

58. vektorlar berilgan. x ning qanday qiymatlarida vektor vektorga perpendikulyar bo`ladi? (97–4–50)
A) -4 B) -6 C) -7 D) -3 E) -5
59. vektorlar berilgan. x ning qanday qiymatida vektor vektorga perpendikulyar bo`ladi? (97–9–110)
A) 1 B) 2 C) 4 D) -1,25 E) -2
60. vektorlar m ning qanday qiymatida perpendikulyar bo`ladi? (98–2–55)
A) 14 B) 16 C) 15 D) -15 E) -14
61. Agar vektorlar o`zaro perpendikulyar bo`lsa, x ning qiymati qanchaga teng bo`ladi? (98–10–30)
A) 0,8 B) 0,6 C) -0,8 D) -0,6 E) 0,5
62. Agar bo`lsa, α ning qanday qiymatlarida vektorlar perpendikulyar bo`ladi? (99–3–41)

63. Trapetsiyada MN o`rta chiziq, AB=12, CD=8 va bo`lsa, λ nimaga teng? (97–5–47)

A) 1,2 B) -1,2 C) 1,5 D) -1,5 E) 2
64. Trapetsiyada MN o`rta chiziq, AB=13, CD=7 va bo`lsa, λ nimaga teng? (97–9–47)

A) 0,6 B) -0,6 C) 0,7 D) -0,7 E) 0,8
65. y=x² parabolani vektor bo`yicha parallel ko`chirganda, uning tenglamasi qanday bo`ladi? (00–2–28)
A) y=x²+6x+11 B) y=x²+5 C) y=x²-1
D) y=x²+9 E) y=x²+4x-9