Vektorning fizik va geometrik talqinlari. Geometrik masalalar yechishning vektor usuli — 8-sinf Geometriya test savollari

1.Parashutchi yerga 4 m/s tezlik bilan tushmoqda, shamol esa uni 4√3 m/s tezlik bilan surib ketmoqda. Parashutchi yerga qanday burchak ostida tushadi?

• A)30°
• B)45°
• C)60°
• D)53°

2.Og'irligi P = 80 N bo'lgan yuk qiya tekislikda turibdi, og'ish burchagi 30°. Yukni ushlab turish uchun kerakli F kuchni toping (F = P·sinα).

• A)40 N
• B)69,3 N
• C)160 N
• D)20 N

3.P = 60 N yuk og'ma tekislikda yotibdi, og'ish burchagi 30°. Bosim kuchini toping.

• A)≈ 52 N
• B)30 N
• C)60 N
• D)45 N

4.C nuqta AB kesmaning o'rtasi, O — ixtiyoriy nuqta. OA(3; -1) va $OB$(5; 7) bo'lsa, $OC$ vektorining koordinatalarini toping.

• A)(4; 3)
• B)(8; 6)
• C)(1; 4)
• D)(4; -3)

5.Uchburchakning uchlari A(3; 1), B(1; 3), C(0; 2). $C{C}_1$ medianasining ($C_1$ — AB tomonining o'rtasi) uzunligini toping.

• A)2
• B)4
• C)√8
• D)1

6.A(2; 4), B(3; 6), C(6; 14) nuqtalar berilgan. AB + AC vektorining koordinatalarini toping.

• A)(5; 12)
• B)(5; -12)
• C)(7; 16)
• D)(3; 8)

7.ABCD kvadratning ikki qarama-qarshi uchi A(0; 4) va C(6; 0) berilgan. Qolgan ikki B va D uchlarining abssissalari yig'indisi va ordinatalari yig'indisini (Bx+Dx; By+Dy) toping.

• A)(6; 4)
• B)(12; 8)
• C)(3; 2)
• D)(6; 8)

8.Kesmani berilgan nisbatda bo'lish: AC = 2·$CB$ bo'lib, A(1; 1), B(7; 10) bo'lsa, C nuqtaning koordinatalarini toping.

• A)(5; 7)
• B)(4; 5,5)
• C)(13; 16)
• D)(5; 5)

9.M1(2; 0) nuqtaga m1 = 3 birlik, M2(10; 8) nuqtaga m2 = 1 birlik massa qo'yilgan. Bu sistemaning og'irlik markazi C ning koordinatalarini toping.

• A)(4; 2)
• B)(6; 4)
• C)(16; 8)
• D)(5; 4)

10.ABCD parallelogrammda diagonallari O nuqtada kesishadi. OA + $OC$ yig'indisi qanday vektorga teng?

• A)nol vektor
• B)$OB$ + OD
• C)2$OB$
• D)AC vektor