.
, , . .
3.2.
. 30, , 30, , 30. . , 76.
76-2*30=16.
. , , .
3.3.
1
1.1
:
) ;
) ( );
) .
1. | 2. |
3. | 4. |
5. | 6. |
7. | 8. |
9. | 10. |
11. | 12. |
13. | 14. |
15. | 16. |
17. | 18. |
19. | 20. |
21. | 22. |
23. | 24. |
25. | 26. |
27. | 28. |
29. | 30. |
1.2
.
1. | 2. |
3. | 4. |
5. | 6. |
7. | 8. |
9. | 10. |
11. | 12. |
13. | 14. |
15. | 16. |
17. | 18. |
19. | 20. |
21. | 22. |
23. | 24. |
25. | 26. |
27. | 28. |
29. | 30. |
1.3
a, b :
) ;
) a b;
) c d;
) M, l .
1. A (4, 6, 3), B (-5, 2, 6), C (4, -4, -3), a = - , b = , c = , d = , l = AB, = 5, = 4.
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2. A (4, 3, -2), B (-3, -1, 4), C (2, 2, 1), a = , b = , c = , d = , l = BC, = 2, = 3.
3. A (-2, -2, 4), B (1, 3, -2), C (1, 4, 2), a = , b = , c = , d = , l = BA, =2, =1.
4. A (2, 4, 3), B (3, 1, -4), C (-1, 2, 2), a = + , b = , c = b, d = , l = BA, = 1, = 4.
5. A (2, 4, 5), B (1, -2, 3), C (-1, -2, 4), a = , b = , c = b, d = , l = AB, = 2, = 3.
6. A (-1, -2, 4), B (-1, 3, 5), C (1, 4, 2), a = , c = b = , d = , l = AC, = 1, = 7.
7. A (1, 3, 2), B (2, 4, 1), C (1, 3, 2), a = + , B = , = b, d = , l = AB, = 2, = 4.
8. A (2, -4, 3), B (-3, -2, 4), C (0, 0, -2), a = - , b = c = , d = , l = AC, = 2, = 1.
9. A (3, 4, -4), B (-2, 1, 2), C (2, -3, 1), a = - , b = c = , d = , l = AB, = 2, = 5.
10. A (0, 2, 5), B (2, -3, 4), C (3, 2, -5), a = + , b = c = , d = , l = AC, = 3, = 2.
11. A (-2,-3, -4), B (2, -4, 0), C (1, 4, 5), a = - , b = c = , d= , l =AB, = 4, = 2.
12. A (-2, -3, -2), B (1, 4, 2), C (1, -3, 3), a = - , b = c= , d = , l = BC, = 3, = 1.
13. A (5, 6, 1), B (-2, 4,-1), C (3,-3,3), a = - , b = c = , d = , l = BC, = 3, = 2.
14. A (10, 6, 3), B (-2, 4, 5), C (3, -4, -6), a = - , b = c= , d = , l = AC, = 2, = 4.
15. A (3, 2, 4), B (-2, 1, 3), C (2, -2, -1), a = - , b = , c = , d = , l = AB, = 2, = 5.
16. A (-2, 3, -4), B (3, -1, 2), C (4, 2, 4), a = + , b = c = , d = , l = BC, = 2, = 5.
17. A (4, 5, 3), B (-4, 2, 3), C (5, -6, -2), a = - , b = c= , d = , l = BC, = 5, = 1.
18. A (2, 4, 6), B (-3, 5, 1), C (4, -5, -4), a = + , b = c = , d = , l = BC, = 1, = 3.
19. A (-4, -2, -5), B (3, 7, 2), C (4, 6, -3), a = + , b = c = , d = , l = BA, = 4, = 3.
20. A (5, 4, 4), B (-5, 2, 3), C (4, 2, -5), a = - , b = , c = , d = , l = BC, = 3, = 1.
21. A (3, 4, 6), B (-4, 6, 4), C (5, -2, -3), a = + , b = , c = , d = , l = BA, = 5, = 3.
22. A (-5, -2, -6), B (3, 4, 5), C (2, -5, 4), a = - , b = c = , d = , l = AC, = 3, = 4.
23. A (3, 4, 1), B (5, -2, 6), C (4, 2, -7), a = + , b = c = , d = , l = AB, = 2, = 3.
24. A (4, 3, 2), B (-4, -3, 5), C (6, 4, -3), a = - , b = c = , d = , l = BC, = 2, = 5.
25. A (-5, 4, 3), B (4, 5, 2), C (2, 7, -4), a = + , b = c = , d = , l = BC, = 3, = 4.
26. A (6, 4, 5), B (-7, 1, 8), C (2, -2, -7), a = - , b = , c = , d = , l = AB, = 3, = 2.
27. A (6, 5, -4), B (-5, -2, 2), C (3, -3, 2), a = - , b = c = , d = , l = BC, = 1, = 5.
28. A (-3, -5, 6), B (3, 5, -4), C (2, 6, 4), a = - , b = , c = , d = , l = BA, = 4, = 2.
29. A (3, 5, 4), B (4, 2, -3), C (-2, 4, 7), a = - , b = ,c = d = , l = BA, = 2, = 5.
30. A (4, 6, 7), B (2, -4, 1), C (-3, -4, 2), a = - , b = c = , d = , l = AB, = 3, = 4.
1.4
. : ) ; ) , ; ) , .
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1. a = 2i - 3j + k, b = j + 4k, = 5i + 2j - 3k.
2. = 3i + 4j + k, b = i - 2j + 7k, = 3i - 6j + 21k.
3. a = 2i - 4j - 2k b = 7i + 3j c = 3i + 5j - 7k.
4. = -7i + 2k, b = 2i - 6j + 4k, c = i-3j + 2k.
5. = -4i + 2j - k, b = 3i + 5j - 2k, c = j + 5k.
6. a = 3i - 2j + k, b = 2j - 3k, c = -3i + 2j - k.
7. a = 4i j + 3k, b = 2i + 3j - 5k, c = 7i + 2j + 4k.
8. a = 4i + 2j - 3k, b = 2i + k, = -12i - 6j + 9k.
9. a = -i + 5k, b = -3i + 2j + 2k, = -2i - 4j + k.
10. a = 6i - 4j + 6k, b = 9i - 6j + 9k, = i - 8k.
11. a = 5i - 3j + 4k, b = 2i - 4j - 2k, c = 3i + 5j - 7k.
12. = -4i + 3j - 7k, b = 4i + 6j - 2k, = 6i + 9j - 3k.
13. = -5i + 2j - 2k, b = 7i - 5k, c = 2i + 3j - 2k.
14. a = -4i - 6j + 2k, b = 2i + 3j - k, c = -i + 5j - 3k.
15. a = -4i + 2j - 3k, b = -3j + 5k, = 6i + 6j -4k.
16. = -3i + 8j, b = 2i + 3j - 2k, c = 8i + 12j - 8k.
17. a = 2i - 4j - 2k, b = -9i + 2k, c = 3i + 5j - 7k.
18. a = 9i - 3j + k, b = 3i - 15j + 21k, c = i - 5j + 7k.
19. = -2i + 4j - 3k, b = 5i + j - 2k, c = 7i + 4j k.
20. = -9i + 4j - 5k, b = i - 2j + 4k, c = -5i + 10j - 20k.
21. a = 2i - 7j + 5k, b = -i + 2j - 6k, c = 3i + 2j - 4k.
22. a = 7i - 4j - 5k, b = i - 11j + 3k, = 5i + 5j + 3k.
23. a = 4i - 6j - 2k, b = -2i + 3j + k, c = 3i - 5j + 7k.
24. a = 3i j + 2k, b = -i + 5j - 4k, c = 6i - 2j + 4k.
25. = -3i j - 5k, b = 2i - 4j + 8k, c = 3i + 7j k.
26. = -3i + 2j + 7k, b = i - 5k, c = 6i + 4j k.
27. a = 3i j + 5k, b = 2i - 4j + 6k, c = i - 2j + 3k.
28. a = 4i - 5j - 4k, b = 5i - j, c = 2i + 4j - 3k.
29. = -9i + 4k, b = 2i - 4j + 6k, c = 3i - 6j + 9k.
30. a = 5i - 6j - 4k, b = 4i + 8j - 7k, c = 3j - 4k.
1.5
1(), 2(), A3() 4(). :
) 1 2 3;
) 1 2;
) 4 , 1 2 3;
) 3 N, 1 2;
) , 4 1 2.
:
) 1 4 1 2 3.
) 1 2 3.
1. 1(3, 1, 4), 2(-1, 6, 1), 3(1, 1, 6), 4(0, 4, -1).
2. 1(3, 5, 4), 2(5, 8, 3), 3(1, 2, -26), 4(-1, 0, 2).
3. 1(2, 4, 3), 2(1, 1, 5), 3(4, 9, 3), 4(3, 6, 7).
4. 1(9, 5, 5), 2(-3, 7, 1), 3(5, 7, 8), 4(6, 9, 2).
5. 1(0, 7, 1), 2(2, -1, 5), 3(1, 6, 3), 4(3, -9, 8).
6. 1(5, 5, 4), 2(1, -1, 4), 3(3, 5, 1), 4(5, 8, -1).
7. 1(6, 1, 1), 2(4, 6, 6), 3(4, 2, 0), 4(1, 2, 6).
8. 1(7, 5, 3), 2(9, 4, 4), 3(4, 5, 7), 4(7, 9, 6).
9. 1(6, 8, 2), 2(5, 4, 7), 3(2, 4, 7), 4(7, 3, 7).
10. 1(4, 2, 5), 2(0, 7, 1), 3(0, 2, 7), 4(1, 5, 0).
11. 1(4, 4, 10), 2(7, 10, 2), 3(2, 8, 4), 4(9, 6, 9).
12. 1(4, 6, 5), 2(6, 9, 4), 3(2, 10, 10), 4(7, 5, 9).
13. 1(3, 5, 4), 2(8, 7, 4), 3(5, 10, 4), 4(4, 7, 8).
14. 1(10, 9, 6), 2(2, 8, 2), 3(9, 8, 9), 4(7, 10, 3).
15. 1(1, 8, 2), 2(5, 2, 6), 3(5, 7, 4), 4(4, 10, 9).
16. 1(6, 6, 5), 2(4, 9, 5), 3(4, 6, 11), 4(6, 9, 3).
17. 1(7, 2, 2), 2(-5, 7, -7), 3(5, -3, 1), 4(2, 3, 7).
18. 1(8, -6, 4), 2(10, 5, -5), 3(5, 6, -8), 4(8, 10, 7).
19. 1(1, -1, 3), 2(6, 5, 8), 3(3, 5, 8), 4(8, 4, 1).
20. 1(1, -2, 7), 2(4, 2, 10), 3(2, 3, 5), 4(5, 3, 7).
21. 1(4, 2, 10), 2(1, 2, 0), 3(3, 5, 7), 4(2, -3, 5).
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22. 1(2, 3, 5), 2(5, 3, -7), 3(1, 2, 7), 4(4, 2, 0).
23. 1(5, 3, 7), 2(-2, 3, 5), 3(4, 2, 10), 4(1, 2, 7).
24. 1(4, 3, 5), 2(1, 9, 7), 3(0, 2, 0), 4(5, 3, 10).
25. 1(3, 2, 5), 2(4, 0, 6), 3(2, 6, 5), 4(6, 4, -1).
26. 1(2, 1, 6), 2(1, 4, 9), 3(2, -5, 8), 4(5, 4, 2).
27. 1(2, 1, 7), 2(3, 3, 6), 3(2, -3, 9), 4(1, 2, 5).
28. 1(2, -1, 7), 2(6, 3, 1), 3(3, 2, 8), 4(2, -3, 7).
29. 1(0, 4, 5), 2(3, -2, 1), 3(4, 5, 6), 4(3, 3, 2).
30. 1(3, -1, 2), 2(-1, 0, 1), 3(1, 7, 3), 4(8, 5, 8).
1.6
1. , , (-2, 7, 3) - 4 + 5 z - 1 = 0.
2. , 1 2 , 1(1, 5, 6), 2(-1, 7, 10).
3. (2; 0; -0,5) 4 - 4 + 2 z + 17 = 0.
4. , (2, -3, 5) .
5. , (2, 5, -1).
6. , (2, 5, -1), (-3, 1, 3) .
7. , (3, 4, 0) - 2 = - 3 = z + 1 .
1 2 2
8. , - 3 = = z - 1 + 1 = - 1 = z.
2 1 2 2 1 2
9. , 3 - - 7 z + 9 = 0 , (3, 2, -5).
10. <<>>, (6, -10, 1) = -3, z - = 2.
11. , (2, 3, -4) = (4, 1, -1) b = (2, -1, 2).
12. , (1,1,0), (2,-1,-1) 5 + 2 + 3 z -7= 0.
13. , 2 - 3 + z - 1 = 0 - + 5 z +3 = 0.
14. , (3, -1, 2), (2, 1, 4) = (5, -2, -1).
15. , , (5, -2, 3), (1, -3, 5).
16. , , (2, -3, 3) 3 + - 3 z = 0.
17. , (1, -1, 2) 1 2, 1(2, 3, -4), 2(-1, 2, -3).
18. ,
+ 3 - 2 z + 1 = 0, = t + 7, = t - 2, z = 2 t + 1 .
19. , (3, -4, 1) z.
20. , (3, -5, 2).
21. , (1, 2, 3) N (-3, 4, -5) z.
22. , (2, 3, -1) = t - 3, = 2 t + 5, z = -3 t + 1.
23. (4, -3, 1) - 2 - z - 15 = 0.
24. , - 4 + z - 1 = 0 蠠 2 + + 10 z - 3 = 0 .
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25. , (2, -3, -4) .
26. n
+ 2 - 2 z - 7 = 0?
27. , (2, 3, -1), (1, 1, 4) - 4 + 3 z + 2 = 0.
28. , + 5 - z + 7=0 3 - + 2 z - 3=0.
29. , (2, 3, -5) N (-1, 1, -6) = (4, 4, 3).
30. , 3 - 5 + z - 3 = 0 - 3 + 2 z + 5 = 0 .
1.7
1. , 3 - 2 - 7 = 0 + 3 - 6 = 0 , 3.
2. (-8, 12) , (2, -3) (-5, 1).
3. : (-4, 4), (4, -12) (4, 2) . .
4. , , 2, 2 - = 3.
5. , (2, -3) 2 - = 5 + = 1.
6. , D - , (3, 6), (5, 2), (-1, -3), D (-5, 5).
7. , (3, 1) , (2, 5), (1, 0).
8. , (-2, 1) MN, (-3, -2), N (1, 6).
9. , (2, -1) 頠 - 2 + 3 = 0.
10. D, (-1, -3), (3, 5), (5, 2), D (3, -5).
11. 6 -4 +5=0, 2 +5 + 8=0 , .
12. 4 + = 12, 5 - 4 = 12 + = 6. .
13. : (-6, 2), (2, -2) (1, 2). .
14. , , (-4, 2), (3, -5), (5, 0).
15. , , (2, 3), (0, -3), (6, -3).
16. , , : - 2 - - 3 = 0, - + 5 - 7 = 0, - 3 - 2 + 13 = 0.
17. (3, 1), (-3, -1) (5, -12). , .
18. , 2 + 5 - 8 = 0 2 + 3 + 4 = 0.
19. 3 + 5 - 15 = 0, .
20. : - = 0, + 3 = 0, - - 4 = 0, 3 + - 12 = 0. .
21. , (4, 6), (-4, 0), (-1, -4).
22. (5, 2) : ) ; ) ; ) .
23. , (-2, 3) : ) 450; ) 900; )00.
24. , (-6, -6) (-3, -1) , 3?
25. 2 - 5 - 1 = 0 + 4 - 7 = 0 , (4, -3) (-1, 2) l = 2/3.
26. 2 - 5 - 1 = 0 2 - 5 - 34 = 0 +3 -6=0. .
27. , (-3, 1), (7, 5) (5, -3).
28. , (-1, 1) 450 2 + 3 = 6.
29. 2 -3 +1=0, + 2 + 1 = 0 (2, 3). .
30. - 2 = 0, - - 1 = 0 (3, -1). .
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1.8
().
1. ) 4 2 - 2 - 16 z 2 + 16 = 0; ) 2 + 4 z = 0.
2. ) 3 2 + 2 + 9 z 2 - 9 = 0; ) 2 + 2 2 - 2 z = 0.
3. ) -5 2 + 10 2 - z 2 + 20 = 0; ) 2 + 4 z 2= 5 2.
4. ) 4 2 - 8 2 + z 2 + 24 = 0; ) 2 - = -9 z 2.
5. ) 2 - 6 2 + z 2 = 0; ) 7 2 - 3 2 - z 2= 21.
6. ) z = 8 - 2 - 4 2; ) 4 2 + 9 2 + 36 z 2= 72.
7. ) 4 2 + 6 2 - 24 z 2 = 96; ) 2 + 8 z 2= = 20 2.
8. ) 4 2 - 5 2 - 5 z 2 + 40 = 0; ) = 5 2 + 3 z 2.
9. ) 2 = 8( 2 + z 2); ) 2 2 + 3 2 - z 2= 18.
10. ) 5 z 2 + 2 2 = 10 ; ) 4 z 2 - 3 2 - 5 2 + 60 = 0.
11. ) 2 - 7 2 - 14 z 2 - 21 = 0; ) 2 = 2 + 4 z 2.
12. ) 6 2 - 2 + 3 z 2 - 12 = 0; ) 8 2 + 2 z 2 = .
13. ) -16 2 + 2 + 4 z 2 - 32 = 0; ) 6 2 + 2 - 3 z 2 = 0.
14. ) 5 2 - 2 - 15 z 2 + 15 = 0; ) 2 + 3 z = 0.
15. ) 6 2 + 2 + 6 z 2 - 18 = 0; ) 3 2 + 2 - 3 z = 0.
16. ) -7 2 + 14 2 - z 2 + 21 = 0; ) 2 + 2 z 2 = 6 2.
17. ) -3 2 + 6 2 - z 2 - 18 = 0; ) 2 - 2 = - z 2.
18. ) 4 2 - 6 2 + 3 z 2 = 0; ) 4 2 - 2 - 3 z 2 = 12.
19. ) z = 4 - 2 - 2; ) 3 2 + 12 2 + 4 z 2 = 48.
20. ) 4 2 + 5 2 - 10 z 2 = 60; ) 7 2 + z 2 = 14 2.
21. ) 9 2 - 6 2 - 6 z 2 + 1 = 0; ) 15 = 10 2 + 6 2.
22. ) 2 = 5 ( 2 + z 2); ) 2 2 + 3 2 - z 2 = 36.
23. ) 4 2 + 3 2 = 14 ; ) 3 2 - 4 2 - 2 z 2 + 12 = 0.
24. ) 8 2 - 2 - 2 z 2 - 32 = 0; ) - 4 z 2 = 3 2.
25. ) 2 - 6 2 + z 2 - 12 = 0; ) - 3 z 2 = 9 2.
26. ) 2 2 - 3 2 - 5 z 2 + 30 = 0; ) 2 2 + 3 z = 0.
27. ) 7 2 + 2 2 + 6 z 2 - 42 = 0; ) 2 2 + 4 2 - 5 z = 0.
28. ) -4 2 + 12 2 - 3 z 2 + 24 = 0; ) 2 2 + 6 z 2 = 3 .
29. ) 3 2 - 9 2 + z 2 + 27 = 0; ) z 2 - 2 = -4 2.
30. ) 27 2 - 63 2 + 21 z 2 = 0; ) 3 2 - 7 2 - 2 z 2 = 42.
2
2.1
.
1. .
2. .
3. .
4. .
5. .
6. .
7. .
8. .
9. .
10. .
12. .
13. .
14. .
15. .
18. .
22.
27.
28.
29.
30.
2.2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
2.3
, .
16.
17.
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: 2018-10-14; !; : 197 |
:
, .
==> ...