Нач Геом ПРЗ
.pdfЗадача 27. Построить линию пересечения заданных плоскостей.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
90 |
60 |
90 |
90 |
60 |
90 |
60 |
90 |
90 |
60 |
90 |
90 |
90 |
55 |
10 |
40 |
10 |
40 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
35 |
80 |
45 |
35 |
90 |
60 |
95 |
65 |
30 |
90 |
75 |
40 |
60 |
20 |
40 |
70 |
35 |
75 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
70 |
40 |
70 |
60 |
30 |
65 |
25 |
55 |
50 |
10 |
65 |
60 |
70 |
10 |
65 |
10 |
40 |
5 |
P2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
x |
10 |
10 |
40 |
10 |
10 |
10 |
45 |
10 |
40 |
10 |
10 |
40 |
10 |
40 |
90 |
90 |
80 |
55 |
Qx |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
55 |
50 |
90 |
35 |
40 |
30 |
10 |
30 |
60 |
30 |
40 |
70 |
35 |
75 |
75 |
40 |
30 |
20 |
Q1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
35 |
70 |
10 |
25 |
30 |
40 |
80 |
65 |
20 |
55 |
65 |
10 |
40 |
5 |
35 |
30 |
70 |
10 |
Q2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
90 |
60 |
90 |
90 |
60 |
90 |
60 |
90 |
90 |
60 |
90 |
90 |
90 |
55 |
10 |
40 |
10 |
40 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
70 |
40 |
70 |
60 |
30 |
65 |
25 |
45 |
50 |
10 |
65 |
60 |
70 |
90 |
65 |
10 |
40 |
5 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
35 |
80 |
45 |
35 |
90 |
60 |
95 |
65 |
30 |
90 |
75 |
40 |
60 |
20 |
40 |
70 |
35 |
75 |
P2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
x |
10 |
10 |
40 |
10 |
10 |
10 |
45 |
10 |
40 |
10 |
10 |
40 |
10 |
40 |
90 |
90 |
90 |
60 |
Qx |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
35 |
70 |
10 |
25 |
60 |
40 |
80 |
65 |
20 |
55 |
65 |
10 |
40 |
5 |
65 |
60 |
70 |
90 |
Q1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
55 |
50 |
90 |
35 |
40 |
30 |
10 |
30 |
60 |
30 |
40 |
70 |
35 |
75 |
75 |
40 |
60 |
20 |
Q2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
Задача 28. Построить линию пересечения заданных плоскостей.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
45 |
40 |
85 |
50 |
80 |
40 |
85 |
85 |
45 |
80 |
45 |
85 |
85 |
85 |
5 |
20 |
85 |
10 |
A |
y |
5 |
15 |
0 |
15 |
20 |
15 |
10 |
0 |
25 |
5 |
35 |
0 |
15 |
0 |
10 |
40 |
5 |
5 |
|
z |
35 |
15 |
40 |
25 |
10 |
30 |
15 |
0 |
20 |
40 |
10 |
40 |
10 |
0 |
15 |
35 |
40 |
40 |
|
x |
5 |
20 |
45 |
10 |
60 |
5 |
40 |
70 |
5 |
40 |
30 |
50 |
60 |
70 |
30 |
5 |
45 |
30 |
B |
y |
10 |
40 |
25 |
5 |
0 |
0 |
5 |
40 |
0 |
15 |
0 |
15 |
0 |
35 |
35 |
0 |
25 |
35 |
|
z |
15 |
35 |
20 |
40 |
40 |
40 |
35 |
35 |
40 |
25 |
40 |
30 |
35 |
40 |
0 |
0 |
20 |
5 |
|
x |
30 |
5 |
70 |
30 |
45 |
20 |
60 |
45 |
20 |
60 |
10 |
70 |
50 |
45 |
40 |
45 |
70 |
50 |
C |
y |
35 |
0 |
40 |
35 |
35 |
40 |
35 |
15 |
40 |
35 |
20 |
40 |
35 |
15 |
5 |
15 |
40 |
15 |
|
z |
0 |
0 |
0 |
5 |
10 |
5 |
0 |
15 |
0 |
5 |
10 |
5 |
5 |
15 |
35 |
15 |
0 |
25 |
|
x |
85 |
85 |
70 |
85 |
10 |
80 |
5 |
5 |
80 |
5 |
80 |
10 |
5 |
5 |
85 |
85 |
10 |
85 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
50 |
65 |
25 |
60 |
25 |
65 |
40 |
25 |
65 |
30 |
65 |
25 |
35 |
50 |
50 |
65 |
25 |
60 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
55 |
40 |
45 |
50 |
35 |
50 |
35 |
50 |
45 |
40 |
55 |
40 |
40 |
25 |
55 |
40 |
45 |
50 |
P2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
45 |
80 |
45 |
85 |
45 |
40 |
85 |
50 |
80 |
40 |
80 |
50 |
80 |
80 |
30 |
10 |
70 |
30 |
A |
y |
20 |
40 |
10 |
40 |
35 |
15 |
40 |
25 |
10 |
30 |
20 |
0 |
10 |
5 |
5 |
10 |
5 |
0 |
|
z |
25 |
5 |
35 |
0 |
5 |
15 |
0 |
15 |
20 |
15 |
0 |
10 |
25 |
20 |
35 |
20 |
40 |
35 |
|
x |
20 |
60 |
10 |
70 |
30 |
20 |
70 |
30 |
45 |
20 |
60 |
30 |
40 |
60 |
40 |
30 |
50 |
5 |
B |
y |
0 |
5 |
10 |
5 |
0 |
35 |
0 |
5 |
10 |
5 |
0 |
40 |
20 |
35 |
25 |
40 |
30 |
15 |
|
z |
40 |
35 |
20 |
40 |
35 |
40 |
40 |
35 |
35 |
40 |
40 |
40 |
35 |
40 |
15 |
0 |
10 |
10 |
|
x |
5 |
40 |
30 |
50 |
5 |
5 |
45 |
10 |
60 |
5 |
40 |
10 |
60 |
45 |
80 |
45 |
85 |
40 |
C |
y |
40 |
25 |
40 |
30 |
15 |
0 |
20 |
40 |
40 |
40 |
40 |
10 |
40 |
15 |
40 |
10 |
40 |
35 |
|
z |
0 |
15 |
0 |
15 |
10 |
0 |
25 |
5 |
0 |
0 |
20 |
5 |
0 |
5 |
0 |
35 |
0 |
5 |
|
x |
80 |
5 |
80 |
10 |
85 |
85 |
10 |
85 |
10 |
80 |
10 |
80 |
10 |
15 |
5 |
80 |
10 |
85 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
45 |
40 |
55 |
40 |
55 |
40 |
45 |
50 |
35 |
50 |
50 |
40 |
20 |
30 |
40 |
55 |
40 |
55 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
65 |
30 |
65 |
25 |
50 |
65 |
25 |
60 |
25 |
65 |
40 |
50 |
60 |
45 |
30 |
65 |
25 |
50 |
P2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
Задача 29. Построить линию пересечения заданных плоскостей.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
90 |
90 |
95 |
90 |
95 |
95 |
95 |
90 |
90 |
90 |
95 |
95 |
90 |
90 |
60 |
60 |
75 |
70 |
A |
y |
15 |
20 |
20 |
15 |
45 |
30 |
20 |
5 |
10 |
35 |
25 |
35 |
0 |
30 |
10 |
10 |
0 |
5 |
|
z |
0 |
30 |
5 |
35 |
25 |
35 |
25 |
20 |
20 |
15 |
45 |
30 |
15 |
20 |
30 |
30 |
40 |
25 |
|
x |
85 |
75 |
85 |
75 |
85 |
65 |
85 |
70 |
75 |
95 |
65 |
65 |
85 |
70 |
70 |
75 |
65 |
60 |
B |
y |
85 |
75 |
85 |
70 |
85 |
65 |
85 |
70 |
75 |
95 |
65 |
65 |
85 |
70 |
70 |
75 |
60 |
60 |
|
z |
25 |
45 |
35 |
35 |
45 |
25 |
45 |
40 |
40 |
40 |
40 |
25 |
30 |
40 |
5 |
0 |
10 |
10 |
|
x |
70 |
70 |
65 |
95 |
65 |
85 |
70 |
90 |
65 |
70 |
85 |
85 |
70 |
75 |
90 |
90 |
90 |
30 |
C |
y |
5 |
40 |
10 |
40 |
40 |
0 |
25 |
25 |
20 |
35 |
45 |
0 |
5 |
45 |
5 |
25 |
15 |
20 |
|
z |
5 |
20 |
15 |
15 |
10 |
0 |
20 |
10 |
15 |
15 |
5 |
0 |
5 |
5 |
20 |
15 |
25 |
5 |
|
x |
40 |
40 |
45 |
45 |
35 |
45 |
40 |
40 |
45 |
45 |
35 |
45 |
40 |
40 |
10 |
10 |
30 |
40 |
D |
y |
20 |
40 |
15 |
35 |
40 |
20 |
5 |
20 |
15 |
5 |
0 |
30 |
25 |
0 |
25 |
5 |
5 |
30 |
|
z |
25 |
0 |
20 |
5 |
0 |
30 |
5 |
40 |
10 |
35 |
40 |
30 |
20 |
40 |
15 |
20 |
25 |
10 |
|
x |
25 |
20 |
35 |
35 |
20 |
25 |
25 |
10 |
25 |
15 |
5 |
25 |
25 |
10 |
25 |
30 |
10 |
25 |
E |
y |
45 |
10 |
40 |
10 |
5 |
25 |
35 |
30 |
35 |
0 |
15 |
45 |
45 |
5 |
40 |
25 |
20 |
0 |
|
z |
45 |
25 |
45 |
25 |
45 |
45 |
30 |
20 |
45 |
20 |
35 |
35 |
45 |
20 |
0 |
5 |
5 |
40 |
|
x |
5 |
10 |
10 |
10 |
5 |
15 |
10 |
35 |
15 |
35 |
20 |
15 |
5 |
20 |
40 |
40 |
40 |
10 |
F |
y |
25 |
20 |
20 |
20 |
35 |
5 |
0 |
45 |
5 |
25 |
45 |
15 |
20 |
25 |
10 |
10 |
30 |
15 |
|
z |
20 |
5 |
10 |
0 |
15 |
15 |
15 |
5 |
20 |
10 |
5 |
5 |
25 |
10 |
30 |
30 |
10 |
25 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
85 |
40 |
45 |
45 |
95 |
95 |
95 |
95 |
95 |
90 |
90 |
95 |
95 |
95 |
90 |
90 |
90 |
90 |
A |
y |
30 |
40 |
15 |
35 |
5 |
0 |
15 |
15 |
25 |
20 |
20 |
20 |
35 |
5 |
20 |
15 |
25 |
5 |
|
z |
25 |
0 |
20 |
5 |
20 |
20 |
35 |
5 |
20 |
5 |
10 |
0 |
15 |
15 |
5 |
25 |
15 |
20 |
|
x |
70 |
20 |
35 |
35 |
85 |
65 |
75 |
85 |
85 |
90 |
75 |
75 |
90 |
85 |
70 |
75 |
60 |
60 |
B |
y |
5 |
10 |
40 |
10 |
35 |
5 |
0 |
45 |
45 |
10 |
40 |
10 |
5 |
35 |
5 |
0 |
10 |
10 |
|
z |
5 |
25 |
45 |
25 |
45 |
35 |
40 |
35 |
45 |
25 |
45 |
25 |
45 |
45 |
25 |
40 |
30 |
30 |
|
x |
90 |
10 |
10 |
10 |
65 |
75 |
90 |
65 |
70 |
70 |
65 |
65 |
75 |
65 |
60 |
60 |
75 |
70 |
C |
y |
15 |
20 |
20 |
20 |
15 |
25 |
45 |
30 |
20 |
40 |
15 |
35 |
40 |
30 |
30 |
30 |
40 |
25 |
|
z |
0 |
5 |
10 |
0 |
10 |
10 |
5 |
30 |
25 |
0 |
20 |
5 |
0 |
30 |
10 |
10 |
0 |
5 |
|
x |
25 |
90 |
95 |
90 |
45 |
40 |
45 |
45 |
40 |
40 |
45 |
40 |
45 |
45 |
40 |
40 |
40 |
40 |
D |
y |
45 |
20 |
20 |
15 |
20 |
35 |
10 |
25 |
5 |
40 |
10 |
15 |
40 |
25 |
30 |
30 |
10 |
10 |
|
z |
45 |
30 |
5 |
35 |
15 |
15 |
40 |
25 |
5 |
20 |
15 |
35 |
10 |
25 |
10 |
10 |
30 |
30 |
|
x |
5 |
75 |
85 |
70 |
35 |
15 |
5 |
15 |
25 |
35 |
25 |
10 |
25 |
15 |
25 |
30 |
10 |
10 |
E |
y |
25 |
5 |
45 |
15 |
45 |
15 |
25 |
35 |
30 |
5 |
45 |
15 |
5 |
30 |
0 |
5 |
5 |
25 |
|
z |
20 |
45 |
35 |
35 |
40 |
40 |
45 |
30 |
25 |
45 |
35 |
35 |
45 |
35 |
40 |
25 |
20 |
15 |
|
x |
40 |
70 |
65 |
95 |
10 |
10 |
35 |
25 |
10 |
15 |
15 |
10 |
5 |
25 |
10 |
10 |
30 |
25 |
F |
y |
20 |
40 |
10 |
40 |
10 |
35 |
45 |
0 |
15 |
20 |
20 |
40 |
15 |
0 |
15 |
15 |
25 |
40 |
|
z |
25 |
20 |
15 |
15 |
20 |
15 |
5 |
0 |
0 |
30 |
5 |
15 |
25 |
0 |
25 |
5 |
5 |
0 |
Задача 30. Найти точку пересечения прямой DE с плоскостью треугольника ABC и определить видимость прямой относительно плоскости.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
|
7 |
|
8 |
|
9 |
|
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
||||
|
x |
50 |
45 |
50 |
50 |
50 |
55 |
50 |
50 |
50 |
50 |
50 |
55 |
50 |
50 |
50 |
55 |
50 |
50 |
||||||||
A |
y |
35 |
5 |
0 |
30 |
0 |
35 |
20 |
10 |
15 |
35 |
20 |
25 |
15 |
35 |
10 |
30 |
0 |
25 |
||||||||
|
z |
5 |
20 |
20 |
0 |
30 |
10 |
15 |
35 |
35 |
10 |
35 |
0 |
|
20 |
10 |
35 |
0 |
30 |
0 |
|||||||
|
x |
35 |
10 |
10 |
35 |
5 |
25 |
25 |
15 |
10 |
25 |
10 |
35 |
10 |
35 |
10 |
35 |
10 |
25 |
||||||||
B y |
0 |
10 |
15 |
0 |
20 |
0 |
0 |
5 |
0 |
0 |
0 0 |
5 0 |
0 |
0 |
10 |
0 |
|||||||||||
|
z |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
20 |
20 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
||||||||
|
x |
10 |
25 |
25 |
10 |
35 |
10 |
10 |
35 |
35 |
10 |
25 |
5 |
|
25 |
15 |
25 |
5 |
35 |
10 |
|||||||
C |
y |
20 |
35 |
35 |
35 |
35 |
25 |
35 |
35 |
35 |
30 |
35 |
35 |
35 |
20 |
35 |
35 |
35 |
35 |
||||||||
|
z |
15 |
0 |
0 |
10 |
0 |
0 |
|
5 |
|
0 |
|
0 |
|
0 |
|
0 |
10 |
0 |
5 |
|
0 |
|
20 |
0 |
15 |
|
|
x |
60 |
50 |
55 |
55 |
45 |
50 |
5 |
|
55 |
55 |
50 |
45 |
55 |
0 |
35 |
50 |
45 |
55 |
55 |
|||||||
D |
y |
10 |
30 |
25 |
25 |
30 |
10 |
25 |
10 |
5 |
|
10 |
0 |
35 |
10 |
10 |
0 |
|
35 |
25 |
15 |
||||||
|
z |
10 |
30 |
15 |
25 |
35 |
0 |
|
30 |
10 |
15 |
5 |
|
5 |
25 |
10 |
10 |
10 |
30 |
25 |
25 |
||||||
|
x |
5 |
5 |
5 |
10 |
15 |
5 |
|
0 |
|
10 |
5 |
|
5 |
|
15 |
10 |
35 |
10 |
5 |
|
15 |
10 |
5 |
|||
E |
y |
25 |
10 |
5 |
10 |
0 |
35 |
10 |
30 |
25 |
25 |
30 |
10 |
30 |
30 |
25 |
5 |
5 |
15 |
||||||||
|
z |
30 |
10 |
15 |
5 |
5 |
25 |
10 |
30 |
15 |
25 |
35 |
0 |
|
25 |
30 |
35 |
0 |
10 |
5 |
|||||||
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
||||||||
|
x |
50 |
50 |
55 |
50 |
50 |
45 |
50 |
50 |
50 |
55 |
50 |
50 |
55 |
55 |
50 |
50 |
55 |
55 |
||||||||
A |
y |
35 |
10 |
35 |
0 |
5 |
20 |
20 |
0 |
|
35 |
10 |
20 |
20 |
35 |
0 |
|
20 |
35 |
0 |
30 |
||||||
|
z |
35 |
10 |
25 |
5 |
10 |
25 |
25 |
10 |
35 |
10 |
35 |
20 |
35 |
15 |
25 |
25 |
5 |
35 |
||||||||
|
x |
35 |
10 |
25 |
5 |
10 |
25 |
25 |
10 |
35 |
35 |
35 |
20 |
35 |
15 |
25 |
25 |
5 |
35 |
||||||||
B y |
0 |
10 |
15 |
0 |
20 |
0 |
0 |
5 |
0 |
0 |
0 0 |
5 0 |
0 |
0 |
10 |
0 |
|||||||||||
|
z |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
20 |
20 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
||||||||
|
x |
10 |
25 |
10 |
35 |
35 |
10 |
10 |
35 |
5 |
|
25 |
15 |
35 |
20 |
35 |
10 |
10 |
35 |
10 |
|||||||
C |
y |
20 |
35 |
30 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
20 |
40 |
35 |
25 |
35 |
35 |
||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
10 |
15 |
0 |
|
20 |
0 |
|
20 |
0 |
|
0 |
0 |
|
5 |
|
0 |
0 |
10 |
|||
|
x |
55 |
50 |
45 |
60 |
50 |
55 |
55 |
55 |
45 |
50 |
55 |
60 |
60 |
55 |
5 |
|
50 |
45 |
55 |
|||||||
D |
y |
15 |
5 |
5 |
25 |
10 |
30 |
15 |
25 |
35 |
0 |
|
35 |
20 |
0 |
0 |
|
25 |
10 |
30 |
25 |
||||||
|
z |
5 |
10 |
0 |
35 |
10 |
30 |
25 |
25 |
30 |
10 |
20 |
0 |
|
20 |
35 |
30 |
0 |
35 |
25 |
|||||||
|
x |
5 |
5 |
15 |
10 |
5 |
5 |
|
5 |
|
10 |
15 |
5 |
|
10 |
15 |
15 |
10 |
0 |
|
5 |
15 |
10 |
||||
E |
y |
15 |
25 |
35 |
0 |
30 |
10 |
15 |
5 |
|
15 |
25 |
0 |
20 |
35 |
20 |
10 |
35 |
0 |
10 |
|||||||
|
z |
25 |
25 |
30 |
10 |
25 |
10 |
5 |
|
10 |
5 |
|
35 |
20 |
35 |
20 |
0 |
|
10 |
25 |
5 |
5 |
|||||
Задача 31. Найти точку пересечения прямой AB с плоскостью P.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
45 |
40 |
50 |
45 |
50 |
45 |
45 |
50 |
45 |
45 |
40 |
40 |
45 |
50 |
15 |
40 |
50 |
45 |
A |
y |
5 |
0 |
25 |
5 |
35 |
30 |
35 |
30 |
5 |
15 |
5 |
10 |
10 |
35 |
35 |
20 |
10 |
30 |
|
z |
10 |
10 |
30 |
15 |
30 |
30 |
25 |
35 |
10 |
5 |
15 |
5 |
5 |
30 |
40 |
25 |
20 |
25 |
|
x |
15 |
10 |
15 |
20 |
20 |
20 |
15 |
20 |
10 |
20 |
10 |
15 |
15 |
20 |
45 |
10 |
25 |
15 |
B |
y |
25 |
30 |
10 |
25 |
15 |
10 |
10 |
0 |
30 |
35 |
30 |
30 |
35 |
10 |
5 |
5 |
30 |
10 |
|
z |
35 |
35 |
5 |
35 |
5 |
5 |
5 |
10 |
25 |
25 |
35 |
30 |
25 |
0 |
15 |
0 |
40 |
10 |
|
x |
10 |
5 |
55 |
5 |
55 |
50 |
50 |
55 |
5 |
5 |
5 |
10 |
10 |
55 |
10 |
50 |
55 |
10 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
45 |
55 |
5 |
40 |
10 |
15 |
5 |
5 |
35 |
50 |
30 |
45 |
55 |
35 |
40 |
10 |
5 |
45 |
P1 |
y |
35 |
35 |
35 |
30 |
35 |
35 |
30 |
35 |
35 |
30 |
35 |
35 |
35 |
30 |
35 |
35 |
30 |
30 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
55 |
25 |
25 |
50 |
30 |
30 |
15 |
35 |
55 |
40 |
50 |
30 |
45 |
5 |
50 |
30 |
15 |
30 |
P2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
30 |
35 |
35 |
30 |
35 |
30 |
35 |
35 |
35 |
35 |
30 |
30 |
35 |
35 |
30 |
35 |
35 |
30 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
50 |
40 |
50 |
40 |
45 |
40 |
45 |
40 |
40 |
45 |
55 |
45 |
60 |
45 |
45 |
60 |
10 |
25 |
A |
y |
30 |
35 |
30 |
5 |
5 |
10 |
10 |
25 |
15 |
30 |
35 |
5 |
30 |
5 |
5 |
30 |
35 |
5 |
|
z |
25 |
25 |
35 |
10 |
35 |
0 |
5 |
35 |
5 |
30 |
30 |
5 |
35 |
5 |
5 |
35 |
30 |
5 |
|
x |
15 |
15 |
20 |
15 |
15 |
10 |
10 |
15 |
10 |
20 |
25 |
10 |
25 |
10 |
10 |
25 |
45 |
55 |
B |
y |
5 |
15 |
5 |
30 |
5 |
35 |
25 |
5 |
35 |
5 |
5 |
35 |
5 |
30 |
30 |
5 |
5 |
35 |
|
z |
10 |
5 |
15 |
30 |
10 |
30 |
30 |
15 |
30 |
10 |
5 |
30 |
5 |
35 |
35 |
5 |
5 |
30 |
|
x |
55 |
55 |
5 |
10 |
50 |
5 |
5 |
55 |
5 |
50 |
55 |
15 |
55 |
15 |
10 |
55 |
15 |
55 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
25 |
10 |
30 |
30 |
15 |
15 |
55 |
20 |
50 |
30 |
35 |
35 |
10 |
60 |
50 |
10 |
35 |
35 |
P1 |
y |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
5 |
20 |
10 |
45 |
5 |
55 |
35 |
10 |
30 |
15 |
10 |
60 |
35 |
35 |
35 |
35 |
60 |
10 |
P2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
Задача 32. Найти точку пересечения прямой CD с плоскостью Q.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
45 |
40 |
50 |
45 |
50 |
40 |
40 |
40 |
45 |
45 |
40 |
50 |
45 |
40 |
10 |
20 |
20 |
10 |
C |
y |
10 |
25 |
5 |
0 |
35 |
15 |
10 |
5 |
5 |
5 |
10 |
25 |
30 |
5 |
35 |
15 |
10 |
30 |
|
z |
30 |
5 |
30 |
35 |
10 |
30 |
25 |
25 |
35 |
25 |
25 |
0 |
10 |
25 |
10 |
30 |
25 |
10 |
|
x |
20 |
10 |
15 |
15 |
20 |
10 |
15 |
10 |
10 |
15 |
10 |
20 |
20 |
15 |
40 |
50 |
50 |
40 |
D |
y |
25 |
10 |
35 |
25 |
10 |
25 |
30 |
30 |
30 |
35 |
35 |
15 |
10 |
30 |
10 |
25 |
30 |
5 |
|
z |
10 |
30 |
5 |
5 |
25 |
0 |
10 |
10 |
5 |
0 |
10 |
30 |
25 |
10 |
25 |
0 |
10 |
25 |
|
x |
35 |
25 |
30 |
40 |
30 |
35 |
25 |
25 |
30 |
20 |
30 |
25 |
35 |
20 |
30 |
20 |
35 |
25 |
Qx |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
50 |
10 |
60 |
55 |
15 |
60 |
60 |
55 |
40 |
50 |
45 |
10 |
10 |
55 |
45 |
10 |
10 |
55 |
Q1 |
y |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
10 |
55 |
20 |
10 |
55 |
10 |
10 |
10 |
10 |
50 |
5 |
50 |
50 |
10 |
5 |
50 |
50 |
10 |
Q2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
50 |
45 |
40 |
50 |
40 |
50 |
45 |
45 |
50 |
40 |
50 |
55 |
55 |
50 |
45 |
40 |
35 |
15 |
C |
y |
30 |
35 |
25 |
20 |
25 |
10 |
35 |
25 |
10 |
30 |
5 |
30 |
20 |
25 |
30 |
35 |
25 |
10 |
|
z |
5 |
0 |
10 |
25 |
10 |
30 |
5 |
5 |
35 |
15 |
25 |
10 |
30 |
5 |
5 |
0 |
10 |
30 |
|
x |
15 |
15 |
10 |
20 |
15 |
20 |
10 |
15 |
20 |
10 |
15 |
20 |
20 |
15 |
15 |
10 |
10 |
40 |
D |
y |
5 |
5 |
10 |
30 |
10 |
25 |
5 |
0 |
25 |
0 |
30 |
5 |
25 |
10 |
0 |
5 |
15 |
25 |
|
z |
35 |
25 |
35 |
15 |
30 |
5 |
30 |
35 |
10 |
25 |
10 |
25 |
5 |
30 |
35 |
25 |
35 |
10 |
|
x |
30 |
40 |
30 |
25 |
25 |
35 |
30 |
20 |
30 |
30 |
35 |
35 |
35 |
35 |
30 |
40 |
25 |
25 |
Qx |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
20 |
10 |
5 |
50 |
10 |
60 |
10 |
5 |
55 |
10 |
50 |
20 |
65 |
5 |
20 |
10 |
5 |
10 |
Q1 |
y |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
60 |
55 |
45 |
45 |
60 |
5 |
40 |
50 |
15 |
60 |
5 |
65 |
20 |
50 |
65 |
55 |
45 |
60 |
Q2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
VI. Параллельность прямой и плоскости. Параллельность плоскостей.
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Если в пространстве |
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то на чертеже |
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1. |
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Прямая параллельна плоскости |
проекции этой прямой параллельны проекциям |
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какой-либо прямой, принадлежащей этой |
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плоскости. |
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2. |
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Плоскости параллельны |
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а) проекции соответствующих главных линий |
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этих плоскостей параллельны между собой; |
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б) соответствующие следы этих плоскостей |
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параллельны. |
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Задача 33. Провести через точку M произвольную прямую, параллельную |
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плоскости ABC. |
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№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
|
|
x |
50 |
50 |
50 |
55 |
55 |
50 |
50 |
50 |
55 |
50 |
50 |
50 |
45 |
45 |
30 |
10 |
40 |
30 |
A |
y |
35 |
5 |
20 |
10 |
35 |
15 |
35 |
15 |
15 |
25 |
25 |
5 |
5 |
20 |
35 |
35 |
35 |
5 |
|
|
|
z |
25 |
25 |
5 |
35 |
25 |
10 |
20 |
35 |
10 |
35 |
5 |
20 |
15 |
35 |
5 |
10 |
5 |
10 |
|
|
x |
10 |
10 |
20 |
15 |
15 |
10 |
30 |
10 |
35 |
10 |
30 |
10 |
5 |
5 |
50 |
50 |
55 |
55 |
B |
y |
20 |
15 |
5 |
5 |
20 |
10 |
0 |
0 |
35 |
35 |
5 |
10 |
10 |
35 |
5 |
20 |
10 |
35 |
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|
|
z |
35 |
35 |
35 |
15 |
35 |
35 |
35 |
20 |
35 |
20 |
35 |
35 |
35 |
35 |
25 |
5 |
35 |
25 |
|
|
x |
40 |
30 |
10 |
40 |
30 |
20 |
15 |
35 |
15 |
40 |
10 |
20 |
20 |
25 |
10 |
20 |
15 |
15 |
C |
y |
10 |
35 |
35 |
35 |
5 |
35 |
20 |
35 |
10 |
5 |
35 |
35 |
35 |
5 |
15 |
5 |
5 |
20 |
|
|
|
z |
5 |
5 |
10 |
5 |
10 |
10 |
5 |
5 |
20 |
10 |
15 |
5 |
5 |
10 |
35 |
35 |
15 |
35 |
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x |
5 |
0 |
0 |
60 |
60 |
5 |
55 |
55 |
60 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
60 |
60 |
M |
y |
15 |
15 |
10 |
15 |
30 |
25 |
20 |
10 |
25 |
30 |
15 |
20 |
15 |
30 |
15 |
10 |
15 |
30 |
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z |
30 |
15 |
20 |
15 |
15 |
15 |
25 |
25 |
15 |
15 |
15 |
10 |
15 |
15 |
15 |
20 |
15 |
15 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
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x |
50 |
45 |
50 |
45 |
50 |
50 |
50 |
45 |
55 |
50 |
90 |
90 |
45 |
45 |
10 |
10 |
20 |
25 |
A |
y |
10 |
20 |
0 |
10 |
35 |
35 |
10 |
15 |
25 |
10 |
35 |
5 |
20 |
20 |
35 |
35 |
35 |
5 |
|
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|
z |
35 |
5 |
20 |
20 |
20 |
15 |
15 |
5 |
35 |
15 |
10 |
25 |
5 |
0 |
15 |
5 |
5 |
10 |
|
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x |
10 |
30 |
10 |
25 |
10 |
30 |
10 |
20 |
15 |
20 |
80 |
70 |
20 |
30 |
50 |
50 |
45 |
45 |
B |
y |
15 |
0 |
15 |
35 |
25 |
5 |
5 |
5 |
35 |
10 |
5 |
35 |
5 |
35 |
25 |
5 |
5 |
20 |
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|
z |
10 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
20 |
35 |
35 |
35 |
35 |
35 |
25 |
35 |
35 |
35 |
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x |
40 |
10 |
25 |
5 |
20 |
10 |
40 |
50 |
35 |
10 |
55 |
55 |
10 |
10 |
30 |
10 |
5 |
5 |
C |
y |
35 |
35 |
35 |
15 |
5 |
25 |
35 |
35 |
10 |
35 |
20 |
20 |
35 |
5 |
5 |
10 |
10 |
35 |
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z |
10 |
20 |
5 |
10 |
10 |
5 |
5 |
10 |
5 |
10 |
5 |
0 |
10 |
25 |
35 |
35 |
35 |
35 |
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x |
55 |
5 |
5 |
0 |
55 |
60 |
15 |
5 |
60 |
5 |
60 |
25 |
5 |
60 |
0 |
0 |
0 |
0 |
M |
y |
15 |
20 |
10 |
25 |
30 |
15 |
20 |
15 |
15 |
10 |
10 |
30 |
25 |
25 |
15 |
20 |
15 |
30 |
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z |
10 |
25 |
25 |
15 |
15 |
15 |
10 |
15 |
30 |
15 |
20 |
20 |
25 |
30 |
15 |
10 |
15 |
15 |
Задача 34. Построить следы плоскости Q, проведенной через точку M, параллельно плоскости P.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
20 |
15 |
25 |
35 |
25 |
15 |
40 |
45 |
35 |
25 |
35 |
45 |
20 |
15 |
25 |
25 |
45 |
40 |
M |
y |
35 |
40 |
40 |
35 |
35 |
0 |
35 |
40 |
40 |
35 |
35 |
0 |
40 |
35 |
0 |
35 |
0 |
40 |
|
z |
40 |
35 |
35 |
0 |
35 |
0 |
40 |
35 |
35 |
0 |
35 |
0 |
35 |
40 |
35 |
35 |
0 |
35 |
|
x |
10 |
5 |
100 |
20 |
15 |
50 |
50 |
55 |
45 |
40 |
50 |
10 |
10 |
5 |
15 |
40 |
10 |
10 |
Px |
y |
0 0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
45 |
55 |
60 |
40 |
60 |
25 |
15 |
5 |
10 |
60 |
60 |
35 |
60 |
35 |
60 |
10 |
50 |
60 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
60 |
35 |
60 |
50 |
50 |
50 |
50 |
25 |
25 |
10 |
10 |
60 |
45 |
45 |
60 |
60 |
60 |
35 |
P2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
25 |
25 |
25 |
45 |
40 |
45 |
35 |
35 |
35 |
15 |
65 |
5 |
5 |
65 |
15 |
65 |
10 |
15 |
M |
y |
35 |
0 |
35 |
0 |
40 |
35 |
35 |
0 |
35 |
0 |
25 |
40 |
25 |
40 |
40 |
40 |
25 |
30 |
|
z |
40 |
35 |
35 |
0 |
35 |
40 |
40 |
35 |
35 |
0 |
40 |
25 |
40 |
25 |
20 |
25 |
40 |
40 |
|
x |
15 |
40 |
10 |
10 |
50 |
55 |
45 |
20 |
50 |
50 |
55 |
15 |
15 |
15 |
15 |
15 |
15 |
10 |
Px |
y |
0 0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
60 |
10 |
50 |
60 |
60 |
25 |
25 |
50 |
10 |
10 |
30 |
55 |
45 |
15 |
30 |
15 |
40 |
45 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
60 |
60 |
60 |
35 |
15 |
5 |
15 |
15 |
15 |
25 |
15 |
40 |
55 |
30 |
30 |
30 |
55 |
60 |
P2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
Задача 35. Построить следы плоскости P, проведенной через точку M, параллельно плоскости ABC.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
50 |
50 |
50 |
55 |
55 |
50 |
50 |
50 |
55 |
50 |
50 |
50 |
45 |
45 |
30 |
10 |
40 |
30 |
A |
y |
35 |
5 |
20 |
10 |
35 |
15 |
35 |
15 |
15 |
25 |
25 |
5 |
5 |
20 |
35 |
35 |
35 |
5 |
|
z |
25 |
25 |
5 |
35 |
25 |
10 |
20 |
35 |
10 |
35 |
5 |
20 |
15 |
35 |
5 |
10 |
5 |
10 |
|
x |
10 |
10 |
20 |
15 |
15 |
10 |
30 |
10 |
35 |
10 |
30 |
10 |
5 |
5 |
50 |
50 |
55 |
55 |
B |
y |
20 |
15 |
5 |
5 |
20 |
10 |
0 |
0 |
35 |
35 |
5 |
10 |
10 |
35 |
5 |
20 |
10 |
35 |
|
z |
35 |
35 |
35 |
15 |
35 |
35 |
35 |
20 |
35 |
20 |
35 |
35 |
35 |
35 |
25 |
25 |
35 |
25 |
|
x |
40 |
30 |
10 |
40 |
30 |
20 |
15 |
35 |
15 |
40 |
10 |
20 |
20 |
25 |
10 |
20 |
15 |
15 |
C |
y |
10 |
35 |
35 |
35 |
5 |
35 |
20 |
35 |
10 |
5 |
35 |
35 |
35 |
5 |
15 |
5 |
5 |
20 |
|
z |
5 |
5 |
10 |
5 |
10 |
10 |
5 |
5 |
20 |
10 |
15 |
5 |
5 |
10 |
35 |
35 |
15 |
35 |
|
x |
5 |
0 |
0 |
60 |
60 |
5 |
55 |
55 |
60 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
60 |
60 |
M |
y |
15 |
15 |
10 |
15 |
30 |
15 |
20 |
10 |
25 |
30 |
15 |
20 |
15 |
30 |
15 |
10 |
15 |
30 |
|
z |
30 |
15 |
20 |
15 |
15 |
15 |
25 |
25 |
15 |
15 |
15 |
10 |
15 |
15 |
15 |
20 |
15 |
15 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
50 |
45 |
50 |
45 |
50 |
50 |
50 |
45 |
55 |
50 |
90 |
90 |
45 |
45 |
10 |
10 |
20 |
25 |
A |
y |
10 |
20 |
0 |
10 |
35 |
35 |
10 |
15 |
25 |
10 |
35 |
5 |
20 |
20 |
35 |
35 |
35 |
5 |
|
z |
35 |
5 |
20 |
20 |
20 |
15 |
15 |
5 |
35 |
15 |
10 |
25 |
5 |
0 |
15 |
5 |
5 |
10 |
|
x |
10 |
30 |
10 |
25 |
10 |
30 |
10 |
20 |
15 |
20 |
80 |
70 |
20 |
30 |
50 |
50 |
45 |
45 |
B |
y |
15 |
0 |
15 |
35 |
25 |
5 |
5 |
5 |
25 |
10 |
5 |
35 |
5 |
35 |
25 |
5 |
5 |
20 |
|
z |
10 |
35 |
35 |
35 |
35 |
35 |
35 |
35 |
20 |
35 |
35 |
35 |
35 |
35 |
5 |
20 |
15 |
35 |
|
x |
40 |
10 |
25 |
5 |
20 |
10 |
40 |
5 |
35 |
10 |
55 |
55 |
10 |
10 |
30 |
10 |
5 |
5 |
C |
y |
35 |
35 |
35 |
15 |
5 |
25 |
35 |
35 |
10 |
35 |
20 |
20 |
35 |
5 |
5 |
10 |
10 |
35 |
|
z |
10 |
20 |
50 |
10 |
10 |
5 |
5 |
10 |
5 |
10 |
5 |
0 |
10 |
25 |
35 |
35 |
35 |
35 |
|
x |
55 |
5 |
5 |
0 |
55 |
60 |
15 |
0 |
60 |
5 |
60 |
25 |
5 |
65 |
0 |
0 |
0 |
0 |
M |
y |
15 |
20 |
10 |
25 |
30 |
15 |
20 |
15 |
15 |
10 |
10 |
30 |
25 |
25 |
15 |
20 |
15 |
30 |
|
z |
10 |
25 |
25 |
15 |
15 |
15 |
10 |
15 |
30 |
15 |
20 |
20 |
25 |
30 |
15 |
10 |
15 |
15 |
Задача 36. Через точку M провести прямую, параллельную плоскости P.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
20 |
15 |
25 |
35 |
25 |
15 |
40 |
45 |
35 |
25 |
35 |
45 |
20 |
15 |
25 |
25 |
45 |
40 |
M |
y |
35 |
40 |
40 |
35 |
35 |
0 |
35 |
40 |
40 |
35 |
35 |
0 |
40 |
35 |
0 |
35 |
0 |
40 |
|
z |
40 |
35 |
35 |
0 |
35 |
0 |
40 |
35 |
35 |
0 |
35 |
0 |
35 |
40 |
35 |
35 |
0 |
35 |
|
x |
10 |
5 |
15 |
20 |
10 |
50 |
50 |
55 |
45 |
40 |
50 |
10 |
10 |
5 |
15 |
40 |
10 |
10 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
45 |
55 |
60 |
60 |
60 |
25 |
15 |
5 |
15 |
60 |
60 |
35 |
60 |
35 |
60 |
10 |
50 |
60 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
60 |
35 |
60 |
50 |
50 |
50 |
50 |
25 |
25 |
10 |
10 |
60 |
45 |
55 |
60 |
60 |
60 |
35 |
P2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
25 |
25 |
25 |
45 |
40 |
45 |
35 |
35 |
35 |
15 |
65 |
5 |
5 |
65 |
15 |
15 |
10 |
15 |
M |
y |
35 |
0 |
35 |
0 |
40 |
35 |
35 |
0 |
35 |
0 |
25 |
40 |
25 |
40 |
40 |
40 |
25 |
30 |
|
z |
40 |
35 |
35 |
0 |
35 |
40 |
40 |
35 |
35 |
0 |
40 |
25 |
40 |
25 |
20 |
25 |
40 |
40 |
|
x |
15 |
40 |
10 |
10 |
50 |
55 |
45 |
20 |
50 |
50 |
55 |
15 |
15 |
15 |
15 |
15 |
15 |
10 |
Px |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
60 |
10 |
50 |
60 |
60 |
25 |
20 |
50 |
10 |
10 |
30 |
55 |
40 |
15 |
30 |
15 |
40 |
45 |
P1 |
y |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
60 |
60 |
60 |
35 |
15 |
5 |
15 |
15 |
15 |
25 |
15 |
40 |
55 |
30 |
30 |
30 |
55 |
60 |
P2 |
y |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
z |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |