8. : 1) (5, 7) (2, 3); 2)
( 10, 8) (2, 3); 3) (0, 3) ( 4, 0); 4) (4, 5) (2, 3); 5) ( 10, 10) ( 2, 5); 6) (m, n sina) i (m cosa, n).
9. : 1) (3, 4); 2) (2½, 6); 3) ( + b, a b).
10. , : 1) (4, 5), ( 1, 7), ( 2, 3); 2) (2, 3), (8, 5), ( 7, 3);
3) (0, 0), (15, 8), (5, 7); 4) (3, 0), (3, 11), ( 9, 16).
11. , 8 15, . .
12. , : (1½, 2), (2, 2), ( 3, 10), ( 4½, 6).
13. , : (3, 5), (6, 9), (11, 1), ( 3, 3).
14. , (10, ) (2, 7) 17.
15. (0, 8) (4, 5). , .
16. , 2, (15, 3) (8, 10). .
17. ,
( 4, 12), (8, 4), ( 6, 2).
18. , : 1) (8, 3) (4, 5); 2) ( 5, 2) ( 2, 4); 3) (1½,0) ( 2½, 5).
19. ³ (3, 0) (5, 4) 4 . .
20. : (4, 3),
( 3, 5), (0, 4). .
21. ³ (, 4) ( 6, )
( 1, 1) . .
22. ³ ( 5, 2) (, )
( 1½, 1) . .
23. : (7, 4),
( 4, 6), (2, 5). .
24. : (2, 3) ( 3, 4), . .
25. (2, 3) . (4, 5).
26. ( 3, 1), (3, 2), ?
27. г : . , (2, 3)?
28. , , (2, 5), ( 1, 0), ( 2, 4) . , , (1, 1) .
, . 2931.
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29. , r j : 1) r = 3, j = p/3; 2) r = 5, j = p/4; 3) r = 4,
j = p/2; 4) r = 2, j = p; 5) r = 2, j = ½p; 6) r = 4, j = p.
30. г, , : 1) r = 3cos t; 2) r 2sin2 t = a 2;
3) r 2 = a 2cos2 t; 4) r = a (1 + cos t); 5) r 2cos2 t = a 2.
31. г, , : 1) ; 2) ; 3) ; 4) ; 5) .
̳
32. , ( 2, 1) 30 2 = 3.
33. , 45
3 + 2 = 0 .
34. 3 3 7 = 0 , (3, 4) (7, 2).
35. 2 3 = 5 , 1 5, 3 + 4 =2 , 2 6. , . .
36. , , .
37. . .
38. , (5, 5). .
39. , , 5, (3, 2) ( 5, 4).
40. , (12, 4), , (8, 9) ( 7, 7) 9.
41. , . , .
42. (1, 2), ( 1, 1)
(2, 3). , , , .
43. , .
44. ij 8 15. , .
45. 12, 10. , , .
46. 6 8. , , , .
47. , , . .
48. , : , (2, 3) (7, 5), .
49. (2, 1) , , (5, 2) (7, 5), .
50. , , . , ( 3, 3), (4, 6).
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51. : (3, 3)
(5, 3). .
52. : ( 1, 3)
(3, 1). .
53. , , j . .
54. , . .
55. (3, 4) (1, 2). 45. .
56. . , .
57. , .
58. . , .
59. , , : .
60. (10, 9) . : 1) , ; 2) ; 3) , .
61. (1, 2), ( 1, 1) ( 2, 3). , , , .
62. , , .
63. . ϳ ? ; .
64. (5, 3) . , , .
65. , . .
66. . , , .
67. , , , .
68. (1, 2) . , , , .
69. , .
70. F , N. , N, , , , FN.
71. , 0,6. , .
72. , (2, 3)
(4, 1). .
73. ³ , . .
74. , (5, 7), (2, 2)
( 1, 7), D (7, 18) . , , .
75. . , .
76. . , (5, 12), , .
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77. 60 . . .
78. (1, 3) (2, 2) . .
79. . , .
80. , , 5. , , , , , .
81. , . .
82. . , . ( ).
83. ( 4, 6) . , .
84. . , , , .
85. , . , , , .
86. ( 4, 2) (7, 1).
87. ³, , 10. - , , .
88. , 18, ,
( 1, ). , .
89. (1, 2) . , , , .
90. (3, 4) . , .
91. , : , , .
92. , .
93. . , , .
94. (1, 2), ( 1, 1)
(2, 3). , , , .
95. , . , . , .
96. , . . .
1. , , b , .
2. , .
3. , 1, = 60, = 120 = 120. D (. ).
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4.
1(2, 1, 2) 2(1, 2, 1)
5.
1(1, 1, 2) 2(2, 1, 1), : = 60, = = 90.
6. , , Ð xOy Ð zOx . .
7. ᒺ , 1, 1 2, , , 120, 150 60.
8. , , .
9. , OAEDCBGF D, 1, 2 3, , . 3.70.
10. , .
11. , 1(1, 2, 1) 2( 1, 2, 1), , 1 2, .
12. , 1(1, 2, 1) 2(1, 2, 1), 1 2, .
13. , 1. , , .
14. , , , ( ) l.
15. . (1, 2, 3). .
1 | Y 1 | Z 1 | |
X | |||
Y | |||
Z |
16. , 0( 0, 0, z 0) 1( 1, 1, z 1) .
17. (2, 1, 0) , 2.
18. .
19. ?
20. :
) , , ;
) , , .
21. , , , .
22. , , . , .
23. ,
) 1(2, 1, 1), 2(1, 2, 1) 3(2, 2, 1);
) 1(1, 1, 3), 2(2, 0, 3), 3(1, 1, 1).
24. 1(1, 1, 1), 2(1, 1, 1), 3(1, 1, 1) 4(1, 1, 1).
25. , 2, 3 4.
26. , .
27. ,
(1, 2, 1) Oz , 2 1.
28. , (1, 2, 1) y , 2 3.
29. , , .
30. , .
31. (1, 1, 1) , .
32. (1, 1, 1) 1((2, 2, 2) .
33. (2, 0, 0) 1(0, 2, 0) 45 .
34. ǒ, 1(2, 1, 1), 2(2, 1, 3) .
35. , , , , , .
36. ᒺ , .
37. ᒺ 1(1, 1, 1), 2( 1, 1, 1), 3(1, 1, 1), 4(1, 1, 1).
38. (2, 1, 1) .
39. (1, 2, 1) .
40. ( 0, 0, z 0) , , , .
41. , .
42. , .
43. Oz , .
44. , , .
45. , , , .
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46. ᒺ , , , .
47. , , , .
48. (3, 2, 30), .
49. , (1, 1, 1), 1(2, 1, 1) 2( 1, 1, 2).
50. , 1(1, 1, 2), 2( 1, 2, 1), 3(1, 1, 1).
51. ³, , , . l , .
52. , , .
53. (1, 4, 1) , = 0, , .
54. , .
55. , , . .
56. :
57. ,
.
58.
59.
60. j , .
61. 1(2, 1, 2), 2(1, 2, 1).
62. 1(3, 0, 1), 2( 1, 2, 2).
63. : 1) (2, 1, 3), 1(1, 1, 2);
2) (1, 2, 1), 1(1, 2, 3).
64. : 1) (1, 2, 1), 1(1, 3, 2);
2) (2, 1, 1), 1(3, 1, 1).
65. (1, 2, 1) , .
66. ( 1, 1, 2) , .
67. (1, 2, 1) , :
1) ; 2)
68. (2, 2, 1) , , .
69. (2, 1, 1) ,
,
70. (1, 2, 1) ,
71. (1, 2, 1) , , .
72. (2, 1, 1) , , .
73. (1, 1, 2) , , .
74. (1, 2, 1) ,
75. (2, 1, 1) ,
.
76. ,
(2, 1, 1) .
77. , (1, 1, 2) .
78. , , .
79. , .
80. , , .
81. 1(2, 1, 1), 2( 1, 2, 2), 3(4, 3, 1).
82. , .
83. .
84. (2, 1, 1) .
85. ( 1, 2, 0) .
86. l , .
87. , .
88. , .
89. , (0, 1, 1) , .
90.
91.
= 0, = z z = 0, x + y 1 = 0.
92.
.
93.
94. , .
95. (2, 1, 1) , y, xz, yz.
96. (1, 1, 1) , .
97. , .
98. ,
, , .
99. ,
+ y + z = 0.
100. ,
101. , .
102. , .
103. ,
.
104. , .
105. , , .
106. , xOy .
107. , .
108. , , , .
109. ,
( 1, 1, 1).
110. , (2, 1, 1).
111. , .
112. , (1, 1, 1).
113. , .
114. . , .
.
115. .
116. .
117. .
118. .
119. .
120. .
121. .
122. .
123. .
124. .
125. .
126. .
127. .
128. .
129. .
130. .
131. .
132. .
:
133. .
134. .
135. .
136. , .
137. (a, b, g) , , .
138. , .