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12




12.5 - 12.7 L 1 L 2. :

1) r , ;

2) cosj (j - ) .

12.5. L 1: x + y 1 = 0, L 2: 2 x 2 y + 1 = 0.

12.6. L 1: x + y 1 = 0, L 2: .

12.7. L 1: x + 2 y + 1 = 0, L 2: 2 x 4 y 2 = 0.

12.8. ABC :

A (2, 2), B (6, 1), C ( 2, 0). :

) AB;

) CD hc;

) j CD BM.

12.9. , ( 1, 2) L: x = 2 t, y = 1 6 t. t.

12.10. , M o ( 2, 3) M 1(5, 1) M 2(3, 7).

 

12

12.11. a ?

) 2 x 3 y + 4 = 0 a x 6 y + 7 = 0;

) a x 4 y + 1 = 0 2 x + y + 2 = 0;

) 4 x + y 6 = 0 3 x + a y 2 = 0;

) x a y + 5 = 0 2 x + 3 y + 3 = 0.

12.12. , A (1; 2):

) y = 2 x 7;

) x + 3 y 2 = 0.

12.13. 3 x 2 y + 5 = 0,

x + 2 y 9 = 0 , 2 x + y + 6 = 0. .

12.14. M 2,

M 1( 3; 4) 4 x y 1 = 0.

12.15. , :

2 x + y + 4 = 0, x + 7 y 11 = 0 3 x 5 y 7 = 0.


12

12.1. ( 3/4, 1/2), cos j = 1/ . 12.2. (1, 0), cosj = 2/ .

12.3. ) AB: ; ) CD: , hc = 19/ ;

) cosj = 19/ .

12.5. . 12.6. , r = . 12.7. .

12.8. ) AB: ; ) CD: , hc = 4; ) cos j = 1/ .

12.9. t = 1/2. 12.10. x 4 y + 8 = 0.

12.11. ) 4; 9; ) 8; 2; ) 3/4; 12; ) 3/2; 2/3.

12.12. ) 2 x y + 4 = 0; ) 3 x y + 5 = 0. 12.13. 2 x + y 6 = 0.

12.14. (5; 2). 12.15. 13.

13.

: ; ; , ; , ; ; ; ; .

1. 13.1 - 13.5 13.9 - 13.13 13.17 - 13.23
2. 13.6, 13.7 13.14, 13.15  
3. 13.8 13.16  

13.1. P: 2 x + y z + 1 = 0 M (1, 1, 1). P', M P, r .

13.2. P', M 1(1, 2, 0) M 2(2, 1, 1) P: x + y 1 = 0.

13.3. , M (1, 1, 1) a = (0, 1, 2) b = ( 1, 0, 1).

13.4. , A (1, 2, 0)

B (2, 1, 1) a = (3, 0, 1).

13.5. , A (1, 2, 0), B (2, 1, 1) C (3, 0, 1).

 


 

13.6 13.7 P 1 P 2. r , - .

13.6. P 1: x + 2 y z + 1 = 0, P 2: y + 3 z 1 = 0.

13.7. P 1: 2 x y + z 1 = 0, P 2: 4 x + 2 y 2 z 1 = 0.

13.8. ,

P: 2 x 3 y + 6 z 12 = 0 .

 

 





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