AB. C AB λ = | AC |:| CB |. AC CB (.. C AB), λ +. AC CB (.. C AB), λ .
A (x 1, y 1, z 1), B (x 2, y 2, z 2), C (, , ) :
; ; .
, C AB , λ = 1 C (, , ) :
; ; .
,
,
, .
:
1) ;
2) ;
3) ;
4) ;
5) ;
6) = 0 ↔ ^ , .. .
, .. ,
,
.. .
:
.
A , |S|, ,
.
1
A, B C :
) ;
) ;
) ;
) M, l α: β;
) ;
) .
1.1. A (4, 6, 3), B ( 5, 2, 6), C (4, 4, 3),
= 4 , = , = , = ,
l = AB, α = 5, β = 4.
1.2. A (4, 3, 2), B ( 3, 1, 4), C (2, 2, 1),
= 5 + 2 , = , = , = ,
l = BC, α = 2, β = 3.
1.3. A ( 2, 2, 4), B (1, 3, 2), C (1, 4, 2),
= 2 3 , = , = , = ,
l = BA, α = 2, β = 1.
1.4. A (2, 4, 3), B (3, 1, 4), C ( 1, 2, 2),
= 2 + 4 , = , = , = ,
l = BA, α = 1, β = 4.
1.5. A (2, 4, 5), B (1, 2, 3), C ( 1, 2, 4),
= 3 4 , = , = , = ,
l = AB, α = 2, β = 3.
1.6. A ( 1, 2, 4), B ( 1, 3, 5), C (1, 4, 2),
= 3 7 , = , = , = ,
l = AC, α = 1, β = 7.
1.7. A (1, 3, 2), B ( 2, 4, 1), C (1, 3, 2),
= 2 + 5 , = , = , = ,
l = AB, α = 2, β = 4.
1.8. A (2, 4, 3), B ( 3, 2, 4), C (0, 0, 2),
= 3 4 , = = , = ,
l = AC, α = 2, β = 1.
1.9. A (3, 4, 4), B ( 2, 1, 2), C (2, 3, 1),
= 5 + 4 , = = , = ,
l = BA, α = 2, β = 5.
1.10. A (0, 2, 5), B (2, 3, 4), C (3, 2, 5),
= 3 + 4 , = = , = ,
l = AC, α = 3, β = 2.
1.11. A ( 2, 3, 4), B (2, 4, 0), C (1, 4, 5),
|
|
= 4 8 , = = , = ,
l = AB, α = 4, β = 2.
1.12. A ( 2, 3, 2), B (1, 4, 2), C (1, 3, 3),
= 2 4 , = = , = ,
l = BC, α = 3, β = 1.
1.13. A (5, 6, 1), B ( 2, 4, 1), C (3, 3, 3),
= 3 4 , = = , = ,
l = BC, α = 3, β = 2.
1.14. A (10, 6, 3), B ( 2, 4, 5), C (3, 4, 6),
= 5 2 , = = , = ,
l = CB, α = 1, β = 5.
1.15. A (3, 2, 4), B ( 2, 1, 3), C (2, 2, 1),
= 4 3 , = , = , = ,
l = AC, α = 2, β = 4.
1.16. A ( 2, 3, 4), B (3, 1, 2), C (4, 2, 4),
= 7 + 4 , = = , = ,
l = AB, α = 2, β = 5.
1.17. A (4, 5, 3), B ( 4, 2, 3), C (5, 6, 2),
= 9 4 , = = , = ,
l = BC, α = 5, β = 1.
1.18. A (2, 4, 6), B ( 3, 5, 1), C (4, 5, 4),
= 6 + 2 , = = , = ,
l = BC, α = 1, β = 3.
1.19. A ( 4, 2, 5), B (3, 7, 2), C (4, 6, 3),
= 9 + 3 , = = , = ,
l = BA, α = 4, β = 3.
1.20. A (5, 4, 4), B ( 5, 2, 3), C (4, 2, 5),
= 11 6 , = , = , = ,
l = BC, α = 3, β = 1.
1.21. A (3, 4, 6), B ( 4, 6, 4), C (5, 2, 3),
= 7 + 4 , = , = , = ,
l = BA, α = 5, β = 3.
1.22. A ( 5, 2, 6), B (3, 4, 5), C (2, 5, 4),
= 8 5 , = = , = ,
l = AC, α = 3, β = 4.
1.23. A (3, 4, 1), B (5, 2, 6), C (4, 2, 7),
= 7 + 5 , = = , = ,
l = AB, α = 2, β = 3.
1.24. A (4, 3, 2), B ( 4, 3, 5), C (6, 4, 3),
= 8 5 , = = , = ,
l = BC, α = 2, β = 5.
1.25. A ( 5, 4, 3), B (4, 5, 2), C (2, 7, 4),
= 3 + 2 , = = , = ,
l = BC, α = 3, β = 4.
1.26. A (6, 4, 5), B ( 7, 1, 8), C (2, 2, 7),
= 5 2 , = , = , = ,
l = AB, α = 3, β = 2.
1.27. A (6, 5, 4), B ( 5, 2, 2), C (3, 3, 2),
= 6 3 , = = , = ,
l = BC, α = 1, β = 5.
1.28. A ( 3, 5, 6), B (3, 5, 4), C (2, 6, 4),
= 4 5 , = , = , = ,
l = BA, α = 4, β = 2.
1.29. A (3, 5, 4), B (4, 2, 3), C ( 2, 4, 7),
= 3 4 , = , = , = ,
l = BA, α = 2, β = 5.
1.30. A (4, 6, 7), B (2, 4, 1), C ( 3, 4, 2),
= 5 2 , = = , = ,
l = AB, α = 3, β = 4.
1
A ( 5, 1, 6), B (1, 4, 3) C (6, 3, 9) :
) = 4 + ;
) = ;
) = = ;
) M, l = AB 1:3;
) ;
) .
►) = (6, 3, 3), = (5, 1, 6), 4 + = (29, 11, 6),
;
) : = (29, 11, 6), = (5, 1, 6).
=295 + 11( 1) + ( 6)6 = 98;
)
d = , = (6, 3, 3),
= 30 3 18 = 9, | | = ,
;
) : λ = , . ,
, ,
, ;
) : = (29, 11, 6), = (5, 1, 6), , = 98.
= = = 0,394,
= arccos 0,394;
) : = (6, 3, 3), = .
, , .
:
,
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