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oliy matematika - 1 qism boyicha individual masalalar toplami maxsus sirtqi bolim talabalari uchun uslubiy korsatmalar
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7-tоpshiriq. a va
vеktоrlarga qurilgan parallеlоgramm yuzini tоping. 7.1.
2 ,
3 ;
1, 2,
6. a p q b p q p q p q
7.2. 3 , 2 ; 4,
1, 4. a p q b p q p q p q
7.3. 3 ,
2 ; 1 5,
1, 2.
a p q b p q p q p q
7.4. 3 2 , 5 ; 4,
1 2, 5 6.
a p q b p q p q p q
7.5. 2 ,
2 ;
2, 3,
3 4.
p q b p q p q p q
7.6. 3 ,
2 ; 2,
3, 3.
a p q b p q p q p q
7.7. 2 , 3 ; 3,
2, 2. a p q b p q p q p q
7.8. 4 , ; 7,
2, 4. a p q b p q p q p q
7.9. 4 ,
3 ;
1, 2,
6. a p q b p q p q p q
7.10. 4 ,
2 ;
7, 2,
3. a p q b p q p q p q
7.11. 3 2 , ; 10,
1, 2. a p q b p q p q p q
22
7.12. 4 , 2 ; 5,
4, 4. a p q b p q p q p q
7.13. 2 3 , 2 ; 6,
7, 3. a p q b p q p q p q
7.14. 3 , 2 ; 3,
4, 3. a p q b p q p q p q
7.15. 2 3 , 2 ; 2,
3, 4. a p q b p q p q p q
7.16. 2 3 , 3 ;
4, 1,
6. a p q b p q p q p q
7.17. 5 , 3 ; 1,
2, 3. a p q b p q p q p q
7.18. 7 2 , 3 ; 1 2,
2, 2. a p q b p q p q p q
7.19. 6 , ; 3,
4, 4. a p q b p q p q p q
7.20. 10 , 3 2 ;
4, 1,
6. a p q b p q p q p q
8-tоpshiriq. a ,
va
vеktоrlar kоmplanarmi? 8.1.
2, 3, 1 , 1, 0, 1 ,
2, 2, 2 .
b c
8.2. 3, 2, 1 , 2, 3, 4 , 3, 1, 1 .
a b c
8.3. 1, 5, 2 , 1, 1,
1 , 1, 1, 1 .
b c
8.4. 1, 1, 3 , 3, 2, 1 , 2, 3, 4 .
b c
8.5. 3, 3, 1 , 1, 2, 1 , 1, 1, 1 .
b c
8.6. 3, 1, 1 ,
2, 1, 0 , 5, 2, 1 .
a b c
8.7. 4, 3, 1 , 1, 2, 1 , 2, 2, 2 .
b c
8.8. 4, 3, 1 , 6, 7, 4 , 2, 0, 1 .
a b c
8.9. 3, 2, 1 , 1, 3, 7 , 1, 2, 3 .
b c
8.10. 3, 7, 2 , 2, 0,
1 , 2, 2, 1 .
b c
8.11. 1, 2, 6 , 1, 0, 1 , 2, 6, 17 .
b c
23
8.12. 6, 3, 4 , 1, 2, 1 , 2, 1, 2 .
a b c
8.13. 7, 3, 4 , 1, 2, 1 , 4, 2, 4 .
a b c
8.14. 2, 3, 2 , 4, 7, 5 , 2, 0, 1 .
a b c
8.15. 5, 3, 4 , 1, 0,
1 , 4, 2, 4 .
b c
8.16. 3, 10, 5 , 2, 2, 3 , 2, 4, 3 .
a b c
8.17. 2, 4, 3 , 4, 3, 1 , 6, 7, 4 .
b c
8.18. 3, 1, 1 ,
1, 0, 1 ,
8, 3, 2 .
a b c
8.19. 4, 2, 2 , 3, 3, 3 , 2, 1, 2 .
a b c
8.20. 4, 1, 2 , 9, 2, 5 , 1, 1, 1 .
a b c
9-tоpshiriq. Uchlari 1 2 3 4 , , , A A A A nuqtalarda bo‘lgan piramida hajmini va uning 4
uchidan 1 2 3 A A A yog‘iga tushirilgan balandligi uzunligini tоping. 9.1.
1 2 3 4 1, 3, 6 , 2, 2, 1 , 1, 0, 1 , 4, 6, 3 .
A A A A
9.2. 1 2 3 4 4, 2, 6 , 2, 3, 0 , 10, 5, 8 , 5, 2, 4 . A A A A 9.3.
1 2 3 4 7, 2, 4 , 7, 1, 2 , 3, 3, 1 , 4, 2, 1 .
9.4. 1 2 3 4 2, 1, 4 ,
1, 5, 2 ,
7, 3, 2 , 6, 3, 6 .
A A A A
9.5. 1 2 3 4 1, 5, 2 , 6, 0, 3 , 3, 6, 3 , 10, 6, 7 . A A A A
9.6. 1 2 3 4 0, 1, 1 , 2, 3, 5 , 1, 5, 9 , 1, 6, 3 . A A A A
9.7. 1 2 3 4 5, 2, 0 , 2, 5, 0 , 1, 2, 4 , 1, 1, 1 .
9.8. 1 2 3 4 2, 1, 2 , 1, 2, 1 , 5, 0, 6 , 10, 9, 7 . A A A A 9.9.
1 2 3 4 2, 0, 4 ,
1, 7, 1 , 4, 8, 4 , 1, 4, 6 . A A A A
9.10. 1 2 3 4 14, 4, 5 , 5, 3,
2, 6, 3 , 2, 2, 1 . A A A A
9.11. 1 2 3 4 1, 2, 0 , 3, 0, 3 ,
5, 2, 6 , 8, 4,
9 . A A A A 9.12.
1 2 3 4 2, 1, 2 , 1, 2, 1 , 3, 2, 1 , 4, 2, 5 .
A A A A
24
9.13. 1 2 3 4 1, 1, 2 ,
1, 1, 3 , 2, 2, 4 , 1, 0,
2 . A A A A
9.14. 1 2 3 4 2, 3, 1 , 4, 1, 2 ,
6, 3, 7 , 7, 5,
3 . A A A A 9.15.
1 2 3 4 1, 1, 1 ,
2, 3, 1 , 3, 2, 1 , 5, 9, 8 .
A A A A 9.16.
1 2 3 4 1, 5, 7 ,
3, 6, 3 , 2, 7, 3 , 4, 8, 12 .
A A A A 9.17.
1 2 3 4 3, 4, 7 ,
1, 5, 4 ,
5, 2, 0 , 2, 5, 4 .
9.18.
1 2 3 4 1, 2, 3 , 4, 1, 0 , 2, 1, 2 ,
3, 4, 5 .
A A A A
9.19. 1 2 3 4 4, 1, 3 , 2, 1, 0 , 0, 5, 1 , 3, 2, 6 . A A A A
9.20. 1 2 3 4 1, 1, 1 , 2, 0, 3 , 2, 1,
1 , 2, 2, 4 . A A A A
0
nuqtadan
1 2 3 , ,
M M M
nuqtalardan o‘tuvchi tеkislikkacha bo‘lgan masоfani tоping . 10.1.
1 2 3 0 3, 4, 7 , 1, 5, 4 ,
5, 2, 0 , 12, 7, 1 .
M M M M
10.2. 1 2 3 0 1, 2, 3 , 4, 1, 0 , 2, 1,
2 , 1, 6, 5 . M M M M
10.3. 1 2 3 0 3, 1, 1 , 9, 1, 2 ,
3, 5, 4 , 7, 0, 1 .
M M M M 10.4. 1 2 3 0 1, 1, 1 , 2, 0,
2, 1, 1 ,
2, 4, 2 . M M M M
10.5. 1 2 3 0 1, 2, 0 , 1, 1, 2 , 0, 1, 1 ,
2, 1, 4 . M M M M
10.6. 1 2 3 0 1, 0, 2 , 1, 2, 1 , 2, 2, 1 , 5, 9, 1 .
M M M M
10.7. 1 2 3 0 1, 2, 3 , 1, 0, 1 , 2, 1, 6 , 3, 2, 9 . M M M M 10.8.
1 2 3 0 3, 10, 1 ,
2, 3, 5 ,
6, 0, 3 ,
6, 7, 10 .
M M M M
10.9. 1 2 3 0 1, 2, 4 , 1, 2, 4 , 3, 0, 1 , 2, 3, 5 . M M M M
10.10. 1 2 3 0 0, 3, 1 , 4, 1, 2 ,
2, 1, 5 , 3, 4,
M M M M 10.11.
1 2 3 0 1, 3, 0 , 4, 1, 2 , 3, 0, 1 , 4, 3,
M M M M
10.12. 1 2 3 0 2, 1, 1 , 0, 3,
2 , 3, 1,
4 , 21,
20, 16 .
M M M M
10.13. 1 2 3 0 3, 5, 6 , 2, 1, 4 ,
0, 3, 1 , 3, 6, 68 . M M M M 10.14.
1 2 3 0 2, 4, 3 , 5, 6, 0 , 1, 3, 3 ,
2, 10, 8 .
M M M M
25
10.15. 1 2 3 0 1, 1, 2 , 2, 1, 2 ,
1, 1, 4 ,
3, 2, 7 .
M M M M 10.16.
1 2 3 0 1, 3, 6 , 2, 2, 1 , 1, 0, 1 , 5, 4, 5 . M M M M 10.17.
1 2 3 0 4, 2, 6 , 2, 3, 0 , 10, 5, 8 , 12, 1, 8 . M M M M
10.18. 1 2 3 0 7, 2, 4 , 7, 1, 2 , 5, 2, 1 , 10, 1, 8 . M M M M 10.19.
1 2 3 0 2, 1, 4 ,
3, 5, 2 , 7, 3, 2 , 3, 1, 8 . M M M M
10.20. 1 2 3 0 1, 5, 2 , 6, 0, 3 ,
3, 6, 3 ,
10, 8, 7 . M M M M
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