Текисликда аналитик геометрия элементлари

Misol 2. M₁ (1; 3; -5) va M₂ (2; 4; 2) nuktalardan utuvchi tugri chizik tenglamasini tuzing.
x-1 y-3 z+5
---- = ---- = ----
2-1 4-1 2+5

x-1 y-3 z+5

---- = ---- = ----
1 1 7

Aytaylik bizga L₁: x-x₁ y-y₁ z-z₁

----- = ------ = ------ va
m₁ n₁ p₁

x-x₂ y-y₂ z-z₂

L₂: ----- = ------ = ------ va
m₂ n₂ p₂
tugri chiziklarni kanonik tenglamasi bilan berilgan bulsin. Bu tugri chiziklar orasidagi burchakni topish uchun, bu tugri chiziklarning yunaltiruvchi S₁ va S₂ vektorlar orasidagi burchakni topish kifoyadir:
m₁m₂ + n₁n₂ +P₁P₂
sos  = S₁S₂ / S₁  S₂  = ---------------------------------------------------- ( 16)
 m₁² + n ₁² + P₁² m₂² + n ₂² + P₂²
Misol 3. x-2 y+3 z-5
 =  = 
5 3 -2
x+2 y z-3
va  =  = 
3 2 5 tugri chiziklar orasidagi burchakni toping .
5  3 + 3  2 + ( - 2 )  5 11
sos  = ---------------------------------------------------- = 
 25 + 9 + 4  9 + 4 + 25 38

 = arcsos 11/38


Misol 4. M₁ (1; 2; 3) nuktadan utuvchi va


2x+3u+5z-7=0
3x-4y+z-8=0
tugri chizikka parallel tugri chizik tenglamasini tuzing.


i j k
S=N₁ X N₂ = 2 3 5 = (3+20)i - (2-15)j + (-8-9)k=23i+13j-17k 3 -4 1
Demak tugri chizik tenglamasi:
x-1 y-2 z-3
 =  =  ;
23 13 -17


Misol 5. M₁ (-4; 0; 2) nuktadan utib
x+1 y+1 z
---- = ---- = ---- va
2 3 4

x-2 y-3 z-5

---- = ---- = ----
3 2 2
tugri chizikka perpendikulyar bulgan tugri chizik tenglamasini tuzing.
i j k
S=S₁ X S₂ = 2 3 4 = (6-8)i - (4-12)j + (4-9)k=-2i+8j-5k 3 2 2
Endi tugri chizik tenglamasi
x+4 y z-2
---- = ---- = ---- ;
-2 8 -5