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2
-Топшириқ.
a
ва
b
векторларга қурилган
1
с
ва
2
с
векторларнинг ўзаро коллинеарлигини
текширинг.
№
a
b
1
с
2
с
2.1.
(1, -2, 3)
(3, 0, -1)
2
4
a
b
3
b
a
2.2.
(1, 0, -1)
(-2, 3, 5)
2
a
b
3
a
b
2.3.
(-2, 4, 1)
(1, -2, 7)
5
3
a
b
2
a
b
2.4.
(1, 2, -3)
(2, -1, -1)
4
3
a
b
8
a
b
2.5.
(3, 5, 4)
(5, 9, 7)
2
a
b
3
2
a
b
2.6.
(1, 4, -2)
(1, 1, -1)
a
b
4
2
a
b
2.7.
(1, -2, 5)
(3, -1, 0)
4
2
a
b
2
b
a
2.8.
(3, 4, -1)
(2, -1, 1)
6
3
a
b
2
b
a
2.9.
(2, -3, -2)
(1, 0, 5)
3
9
a
b
3
a
b
2.10.
(-1, 4, 2)
(3, -2, 6)
2
a
b
3
6
b
a
2.11.
(5, 0, -1)
(7, 2, 3)
2
a
b
3
6
b
a
2.12.
(0, 3, -2)
(1, -2, 1)
5
2
a
b
3
5
a
b
2.13.
(-2, 7, -1)
(-3, 5, 2)
2
3
a
b
3
2
a
b
2.14.
(3, 7, 0)
(1, -3, 4)
4
2
a
b
2
b
a
2.15.
(-1, 2, -1)
(2, -7, 1)
6
2
a
b
3
b
a
2.16.
(7, 9, -2)
(5, 4, 3)
4
a
b
4
b
a
2.17.
(5, 0, -2)
(6, 4, 3)
5
3
a
b
6
10
b
a
2.18.
(8, 3, -1)
(4, 1, 3)
2
a
b
2
4
b
a
2.19.
(3, -1, 6)
(5, 7, 10)
4
2
a
b
2
a
b
2.20.
(1, -2, 4)
(7, 3, 5)
6
3
a
b
2
b
a
2.21.
(3, 7, 0)
(4, 6, -1)
3
2
a
b
5
7
a
b
2.22.
(2, -1, 4)
(3, -7, -6)
2
3
a
b
3
2
a
b
2.23.
(5, -1, -2)
(6, 0, 7)
3
2
a
b
4
6
b
a
2.24.
(-9, 5, 3)
(7, 1, -2)
2
a
b
3
5
a
b
2.25.
(4, 2, 9)
(0, -1, 3)
4
3
b
a
4
3
a
b
2.26.
(2, -1, 6)
(-1, 3, 8)
5
2
a
b
2
5
a
b
2.27.
(5, 0, 8)
(-3, 1, 7)
3
4
a
b
12
9
b
a
2.28.
(-1, 3, 4)
(2, -1, 0)
6
2
a
b
3
b
a
2.29.
(4, 2, -7)
(5, 0, -3)
3
a
b
6
2
b
a
2.30.
(2, 0, -5)
(1, -3, 4)
2
5
a
b
5
2
a
b
3-Топшириқ.
АВ
ва
АС
векторлар орасидаги бурчак косинусини топинг.
№
A
B
C
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
3.7.
3.8.
3.9.
3.10.
3.11.
3.12.
3.13.
3.14.
3.15.
3.16.
3.17.
3.18.
3.19.
3.20.
3.21.
3.22.
3.23.
3.24.
3.25.
(6, 5, 1)
(5, 4, 2)
(2, 0, 4)
(1, 2, 3)
(1, -1, 2)
(3, -3, 1)
(4, 2, 1)
(1, 0, 2)
(5, -1, 3)
(0, 8, 1)
(1, 0, 4)
(2, 3, 4)
(1, -2, 3)
(0, -3, 6)
(3, 3, -1)
(-1, 2, -3)
(-4, -2, 0)
(5, 3, -1)
(-3, -7, -6)
(2, -4, 6)
(0, 1, -2)
(3, 3, -1)
(2, 1, -1)
(-1, -2, 1)
(6, 2, -3)
(0, 1, 2)
(1, 2, 3)
(1, 1, 1)
(2, -1, 0)
(5, -6, 2)
(-3, -2, 0)
(0, 4, 5)
(2, 4, 3)
(2, 0, 1)
(2, 1, 1)
(0, 2, 3)
(3, 4, 5)
(0, -1, 2)
(-12, -3, -3)
(5, 5, -2)
(3, 4, -6)
(-1, -2, 4)
(5, 2, 0)
(0, -1, -2)
(0, -2, 4)
(3, 1, 2)
(1, 5, -2)
(6, -1, -4)
(-4, -2, 5)
(6, 3, -2)
(2, 1, 0)
(3, 2, 1)
(3, 2, 1)
(3, 2, 1)
(2, 3, -1)
(5, 0, 2)
(1, 2, 7)
(1, 7, 1)
(3, 1, -1)
(-1, 4, 5)
(-1, 1, 0)
(-4, 5, 6)
(3, -4, 5)
(-9, -3, -6)
(4, 1, 1)
(1, 1, -1)
(3, -2, 1)
(6, 4, -1)
(2, 3, 0)
(6, -8, 10)
(4, 1, 1)
(4, 1, 1)
(4, 2, 1)
(-8, -2, 2)
(7, 3, -3)
3.26.
3.27.
3.28.
3.29.
3.30.
(0, 0, 4)
(2, -8, -1)
(3, -6, 9)
(0, 2, -4)
(3, 3, -1)
(-3, -6, 1)
(4, -6, 0)
(0, 3, 6)
(8, 2, 2)
(5, 1, -2)
(-5, -10, -1)
(-2, -5, -1)
(9, -12, 15)
(6, 2, 4)
(4, 1, 1)
4-
Топшириқ
.
F
куч векторининг йўналтирувчи косинусларини аниқланг. А нуқтага
нисбатан В нуқтага қўйилган
F
куч моментини топинг.
№
F
B
A
4.1.
4.2.
4.3.
4.4.
4.5.
4.6.
4.7.
4.8.
4.9.
4.10.
4.11.
4.12.
4.13.
4.14.
4.15.
4.16.
4.17.
4.18.
4.19.
4.20.
4.21.
4.22.
4.23.
(3, 3, 3)
(4, 4, 4)
(8, -8, 8)
(-2, 2, -2)
(5, 5, 5)
(-3, 3, -3)
(6, 6, 6)
(-4, 4, -4)
(7, 7, 7)
(-5, 5, -5)
(-1, -1, 1)
(3, 3, -3)
(-2, -2, -2)
(4, 4, -4)
(-3, -3, -3)
(5, 5, -5)
(-4, -4, -4)
(6, 6, -6)
(-5, -5, -5)
(7, 7, -7)
(3, -3, 3)
(8, 8, -8)
(4, -4, 4)
(3, -1, 5)
(4, -2, 5)
(10, -8, 1)
(11, -9, 1)
(5, -3, 5)
(12, -10, 1)
(6, -4, 5)
(13, -11, 1)
(7, -5, 5)
(14, -12, 1)
(8, -6, -5)
(0, 1, 2)
(9, -7, 5)
(1, 0, 2)
(10, -8, 5)
(2,-1,2)
(11,-9,5)
(3,-2,2)
(12,-10,5)
(4,-3,2)
(5,-3,1)
(5,-4,2)
(6,-4,1)
(4,-2,3)
(5,-3,3)
(9,-7,3)
(10,-8,3)
(6,-4,3)
(11,-9,3)
(7,-5,3)
(12,-10,3)
(8,-6,3)
(13, -11, 3)
(9, -7, 3)
(2, -1, -2)
(10, -8, 3)
(3, 2, -2)
(11, -9, 3)
(4, -3, 2)
(12, -10, 3)
(5, -4, -2)
(13, -11, 3)
(6, -5, -2)
(4, -2, 3)
(7, -6, -2)
(5, -4, 3)
4.24.
4.25.
4.26.
4.27.
4.28.
4.29.
4.30.
(-2, -2, 2)
(5, -5, 5)
(-3, -3, 3)
(6, -6, 6)
(-4, -4, 4)
(7, -7, 7)
(-5, -5, 5)
(6,-5,2)
(7,-5,1)
(7,-6,2)
(8,-6,1)
(8,-7,2)
(9,-7,1)
(9,-8,2)
(8, -7, -2)
(6, -4, 3)
(9, -8, 2)
(7, -5, 3)
(10, -9, -2)
(8, -6, 3)
(11, -10, 2)
5-
Топшириқ.
a
ва
b
векторларидан
қурилган параллелограммнинг юзасини ҳисобланг
№
a
b
p
q
)
(
q
p
5.1.
q
p
2
q
p
3
1
2
6
5.2.
q
p
3
q
p
2
4
1
4
5.3.
q
p
3
q
p
2
1
5
1
2
5.4.
q
p
2
3
q
p
5
4
1
2
5
6
5.5.
q
p
2
q
p
2
2
3
3
4
5.6.
q
p
3
q
p
2
2
3
3
.5.7.
q
p
2
q
p
3
3
2
2
5.8.
q
p
4
q
p
7
2
4
5.9.
q
p
4
q
p
3
1
2
6
5.10.
q
p
4
q
p
2
7
2
3
5.11.
q
p
2
3
q
p
10
1
2
5.12.
q
p
4
q
p
2
5
4
4
5.13.
q
p
3
2
q
p
2
6
7
3
5.14.
q
p
3
q
p
2
3
4
4
5.15.
q
p
3
2
q
p
2
2
3
6
5.16.
q
p
3
2
q
p
2
3
4
1
6
5.17.
q
p
2
3
q
p
3
2
2
5
6
5.18.
q
p
3
4
q
p
2
1
2
6
5.19.
q
p
q
p
2
5
6
5.20.
q
p
5
q
p
5
5
3
6
5.21.
q
p
3
q
p
3
2
2
4
5.22.
q
p
4
q
p
5
3
2
6
5.23.
q
p
5
q
p
3
1
2
3
5.24.
q
p
2
7
q
p
3
1
2
2
2
5.25.
q
p
6
q
p
3
4
4
5.26.
q
p
10
q
p
2
3
4
1
6
5.27.
q
p
6
q
p
2
3
8
1
2
3
5.28.
q
p
4
3
q
p
2,5
2
2
5.29.
q
p
7
q
p
3
3
1
3
4
5.30.
q
p
3
q
p
3
3
5
2
3
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