vektorlar ustida amallar
![Vek t orlar
ust ida amallar](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_1.png)
![№ 1 Koordinat a nuqt alari
A(2;3;4)z
x yO
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|1. A nuqtani qurishni uning koordinatalari bo'yicha (2; 3; 4)
tushuntiring
2. B, C, D, K nuqtalarning koordinatalarini ayting B
C DK](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_2.png)
![№ 2. Koordinatalari berilgan
vektorlar ustida amallar
kzzjyyixx kzjyiхkzjyiхba zyxmma zzyyxxddba zzyyxxccba zyxbzyxa zyxakzjyiха
212121 222111 111 212121 212121 222111
;;, ;;, ;;, ;;,;; ;;,
](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_3.png)
![Berilgan vektorlar
.3;1;2,2;5;0,0;2;1 cbа
a b c q 2 3
Yechish
Kordinata vektorlari
0; 2;1 , , 4; 10; 0 2 9 ; 3; 6 3 а b с
zyxq ;;
х = 6 + 0 – 1 = 5, у = 3 + 10 + 2 = 15, z = -9 + 4 + 0 = -5
5;15;5 q3. Koordinatalari berilgan vektorlar
ustida amallar
Vektor koordinatalarini toping](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_4.png)
![№ 4. Uchburchak medianalarining
kesishish nuqtasi
М – medianalar kesishish nuqtasi ∆ АВС) (
3
1
ОС ОВ ОА ОМ
333 321321321 zzz
zууу
уххх
х
М O
С
ВА О – fazodagi ixtiyoriy nuqta
А(х
1 ; у
1 ; z
1 ), В(х
2 ; у
2 ; z
2 ),
C(x
3 ; y
3 ; z
3 ), M(x; y; z)](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_5.png)
![Berilgan kub АВС DA
1 B
1 C
1 D
1 ,
АВ = а.
11 11
DВvaDA АСvaВС СВvaВВ
BAиAC CAиAB CAиOA ACиBD CBиAD
11 1111 1 11O
1
С
АВ С
1
А
1
В
1
D D
1 О
1 nuqta –А
1 В
1 С
1 D
1
I. Vektorlar orasidagi burchakni
toping
II. Vektorlarning Skalyar ko’paytirishni
hisoblash:Vektorlar orasidagi burchak
qirralar markazi](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_6.png)
![№ 6. Vektorlar orasidagi burchak . 2; 1; 2 а i
1148)(6667,0
13 2
)cos( 1||,39212|| ,2020112 ||||)cos( 0;0;12;1;2
0222
iaia ia ia ia ia
ia iа
YechishVektor orasidagi burchakni hisoblang
va va](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_7.png)
![№ 8. Kesmalar orasidagi burchak
8 2 47
,
35
4
9 0 1 9 4 1
| 3 ) 3 ( 0 2 1 1|
cos
3; 0;1 , 3 ; 2;1
0
1 1
CB B D
ABCDA
1 B
1 C
1 D
1 , parallelepiped va DA = 1,
DC = 2, DD
1 = 3. СВ
1 va D
1 B kesmalar orasidagi burchakni toping
D
1
A
1
B
1 C
1
D
A C
B1 23 Yechish
Dxyz koordinata sistemasida
D
1 (0;0;3), B(1;2;0)
C(0;2;0), B
1 (1;2;3) kiritamiz
X Z
Y](/data/documents/836e4c21-1d92-4628-a2d1-0c4b5cd48608/page_8.png)
Vek t orlar ust ida amallar
№ 1 Koordinat a nuqt alari A(2;3;4)z x yO || | ||| | | || | | | | | | | | |1. A nuqtani qurishni uning koordinatalari bo'yicha (2; 3; 4) tushuntiring 2. B, C, D, K nuqtalarning koordinatalarini ayting B C DK
№ 2. Koordinatalari berilgan vektorlar ustida amallar kzzjyyixx kzjyiхkzjyiхba zyxmma zzyyxxddba zzyyxxccba zyxbzyxa zyxakzjyiха 212121 222111 111 212121 212121 222111 ;;, ;;, ;;, ;;,;; ;;,
Berilgan vektorlar .3;1;2,2;5;0,0;2;1 cbа a b c q 2 3 Yechish Kordinata vektorlari 0; 2;1 , , 4; 10; 0 2 9 ; 3; 6 3 а b с zyxq ;; х = 6 + 0 – 1 = 5, у = 3 + 10 + 2 = 15, z = -9 + 4 + 0 = -5 5;15;5 q3. Koordinatalari berilgan vektorlar ustida amallar Vektor koordinatalarini toping
№ 4. Uchburchak medianalarining kesishish nuqtasi М – medianalar kesishish nuqtasi ∆ АВС) ( 3 1 ОС ОВ ОА ОМ 333 321321321 zzz zууу уххх х М O С ВА О – fazodagi ixtiyoriy nuqta А(х 1 ; у 1 ; z 1 ), В(х 2 ; у 2 ; z 2 ), C(x 3 ; y 3 ; z 3 ), M(x; y; z)