Нач Геом ПРЗ
.pdfIX. Преобразование плоскостей в частное положение
1.Чтобы преобразовать плоскость общего положения в проецирующее, надо фронталь или горизонталь плоскости преобразовать в проецирующее положение.
2.Чтобы проецирующую плоскость преобразовать в плоскость уровня, надо одним из методов преобразования чертежа расположить прямую, в которую данная плоскость спроецирована, в положение параллельное оси проекций.
Задача 48. Преобразовать плоскость ABC:
а) переменой плоскостей проекций во фронтально-проецирующее положение; б) плоскопараллельным перемещением в горизонтально-проецирующее положение.
|
№ |
1 |
2 |
3 |
4 |
5 |
|
6 |
|
7 |
|
8 |
9 |
|
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
55 |
35 |
55 |
55 |
60 |
30 |
60 |
50 |
60 |
30 |
55 |
35 |
35 |
30 |
50 |
50 |
50 |
50 |
||||
А |
y |
30 |
25 |
25 |
30 |
10 |
10 |
10 |
30 |
25 |
15 |
30 |
10 |
25 |
5 |
10 |
20 |
15 |
15 |
||||
|
z |
0 |
5 |
30 |
15 |
15 |
30 |
15 |
0 |
15 |
10 |
10 |
30 |
5 |
30 |
35 |
15 |
35 |
0 |
||||
|
x |
35 |
20 |
25 |
40 |
30 |
5 |
|
40 |
55 |
40 |
15 |
40 |
15 |
20 |
0 |
15 |
25 |
10 |
35 |
|||
B y |
0 0 |
10 |
5 5 |
5 |
5 |
5 0 |
0 |
0 |
0 |
5 |
10 |
10 |
5 5 |
35 |
|||||||||
|
z |
30 |
30 |
30 |
30 |
30 |
25 |
30 |
20 |
30 |
30 |
30 |
0 |
30 |
15 |
20 |
35 |
20 |
35 |
||||
|
x |
20 |
5 |
45 |
25 |
40 |
10 |
30 |
25 |
30 |
5 |
25 |
5 |
5 |
20 |
35 |
10 |
35 |
15 |
||||
C |
y |
15 |
30 |
0 |
25 |
25 |
30 |
30 |
10 |
30 |
30 |
25 |
30 |
35 |
25 |
35 |
35 |
35 |
0 |
||||
|
z |
10 |
10 |
0 |
5 |
5 |
|
0 |
|
0 |
|
25 |
0 |
|
0 |
5 |
30 |
15 |
5 |
0 |
10 |
0 |
10 |
|
№ |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
||||
|
x |
55 |
20 |
35 |
60 |
30 |
55 |
35 |
55 |
30 |
50 |
50 |
50 |
50 |
50 |
30 |
35 |
35 |
35 |
||||
А |
y |
5 |
5 |
10 |
15 |
10 |
10 |
30 |
15 |
30 |
25 |
15 |
15 |
20 |
10 |
5 |
25 |
10 |
30 |
||||
|
z |
25 |
30 |
25 |
25 |
15 |
30 |
10 |
30 |
5 |
|
5 |
0 |
35 |
15 |
35 |
30 |
5 |
30 |
10 |
|||
|
x |
30 |
0 |
10 |
30 |
5 |
|
25 |
5 |
|
25 |
20 |
50 |
35 |
10 |
25 |
15 |
0 |
20 |
15 |
40 |
||
B |
y |
10 |
10 |
30 |
0 |
0 |
|
5 |
|
30 |
5 |
5 |
|
0 |
35 |
0 |
0 |
10 |
10 |
5 |
0 |
0 |
|
|
z |
30 |
15 |
0 |
30 |
30 |
25 |
35 |
25 |
25 |
30 |
30 |
20 |
35 |
20 |
15 |
30 |
0 |
30 |
||||
|
x |
50 |
30 |
5 |
20 |
15 |
40 |
15 |
30 |
0 |
|
30 |
15 |
35 |
10 |
35 |
20 |
5 |
5 |
25 |
|||
C |
y |
30 |
30 |
5 |
30 |
30 |
30 |
0 |
|
30 |
15 |
30 |
0 |
35 |
35 |
35 |
25 |
30 |
35 |
25 |
|||
|
z |
0 |
0 |
20 |
0 |
0 |
|
0 |
|
0 |
|
35 |
10 |
10 |
10 |
0 |
10 |
0 |
5 |
15 |
30 |
5 |
Задача 49. Определить натуральную величину треугольника ABC: а) способом замены плоскостей проекций; б) способом плоскопараллельного перемещения; в) без преобразования чертежа;
г) вращением вокруг горизонтали или фронтали.
|
№ |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
45 |
95 |
40 |
95 |
40 |
90 |
50 |
95 |
55 |
95 |
40 |
90 |
95 |
45 |
95 |
35 |
90 |
35 |
А |
y |
35 |
20 |
10 |
25 |
15 |
20 |
20 |
10 |
0 |
30 |
5 |
25 |
30 |
0 |
25 |
30 |
10 |
0 |
|
z |
20 |
10 |
20 |
30 |
5 |
25 |
35 |
20 |
35 |
25 |
15 |
20 |
10 |
35 |
35 |
10 |
35 |
15 |
|
x |
5 |
90 |
5 |
75 |
15 |
70 |
5 |
75 |
40 |
75 |
15 |
70 |
75 |
5 |
90 |
25 |
50 |
25 |
B |
y |
20 |
0 |
10 |
35 |
35 |
35 |
30 |
0 |
35 |
20 |
35 |
30 |
20 |
10 |
10 |
10 |
50 |
35 |
|
z |
30 |
35 |
35 |
20 |
35 |
30 |
20 |
35 |
0 |
35 |
35 |
35 |
35 |
20 |
10 |
35 |
10 |
35 |
|
x |
25 |
75 |
20 |
90 |
5 |
25 |
40 |
90 |
5 |
90 |
5 |
85 |
95 |
20 |
75 |
5 |
75 |
10 |
C |
y |
0 |
35 |
35 |
10 |
0 |
0 |
0 |
35 |
15 |
0 |
10 |
0 |
5 |
35 |
35 |
35 |
35 |
15 |
|
z |
5 |
0 |
0 |
0 |
10 |
0 |
0 |
0 |
20 |
10 |
0 |
0 |
0 |
0 |
25 |
15 |
35 |
15 |
|
№ |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
95 |
45 |
95 |
50 |
95 |
45 |
95 |
45 |
95 |
50 |
90 |
45 |
90 |
45 |
95 |
40 |
95 |
40 |
А |
y |
35 |
20 |
10 |
30 |
20 |
35 |
10 |
35 |
0 |
35 |
25 |
10 |
20 |
5 |
20 |
25 |
10 |
35 |
|
z |
10 |
35 |
0 |
35 |
30 |
0 |
35 |
20 |
10 |
30 |
30 |
10 |
25 |
20 |
15 |
5 |
5 |
25 |
|
x |
90 |
5 |
95 |
10 |
75 |
20 |
70 |
5 |
95 |
10 |
45 |
20 |
50 |
5 |
80 |
25 |
95 |
10 |
B |
y |
0 |
30 |
35 |
25 |
35 |
0 |
10 |
25 |
35 |
20 |
35 |
35 |
35 |
20 |
10 |
10 |
35 |
30 |
|
z |
35 |
25 |
35 |
20 |
20 |
35 |
20 |
30 |
35 |
25 |
25 |
35 |
30 |
35 |
35 |
35 |
35 |
35 |
|
x |
80 |
30 |
80 |
35 |
95 |
5 |
90 |
30 |
80 |
35 |
60 |
5 |
65 |
25 |
75 |
10 |
75 |
20 |
C |
y |
20 |
0 |
5 |
0 |
0 |
20 |
35 |
10 |
15 |
0 |
10 |
0 |
0 |
35 |
40 |
35 |
15 |
5 |
|
z |
10 |
10 |
15 |
0 |
5 |
10 |
5 |
5 |
5 |
0 |
0 |
5 |
0 |
0 |
5 |
15 |
15 |
5 |
X. Определение углов
Угол между двумя прямыми можно определить одним из следующих способов: а) Заключением угла в треугольник, определив натуральную величину треугольника, получаем натуральную величину угла.
б) Любым способом преобразования чертежа нужно поставить плоскость угла в положение параллельное какой-либо плоскости проекций.
Задача 50. а) определить величину плоского угла ABC;
б) провести биссектрису угла A треугольника ABC.
|
№ |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
75 |
75 |
70 |
75 |
75 |
75 |
75 |
75 |
70 |
75 |
75 |
75 |
75 |
75 |
50 |
50 |
50 |
50 |
А |
y |
10 |
25 |
40 |
10 |
20 |
40 |
20 |
40 |
0 |
10 |
15 |
25 |
10 |
25 |
10 |
40 |
30 |
15 |
|
z |
20 |
40 |
0 |
10 |
15 |
25 |
10 |
25 |
40 |
10 |
20 |
40 |
15 |
40 |
0 |
25 |
30 |
35 |
|
x |
35 |
45 |
40 |
40 |
35 |
45 |
35 |
45 |
40 |
40 |
35 |
45 |
55 |
45 |
20 |
10 |
10 |
10 |
B |
y |
40 |
5 |
5 |
40 |
5 |
10 |
40 |
5 |
40 |
40 |
40 |
0 |
40 |
50 |
20 |
15 |
0 |
40 |
|
z |
40 |
5 |
40 |
40 |
40 |
0 |
40 |
5 |
5 |
40 |
5 |
10 |
40 |
5 |
35 |
40 |
40 |
30 |
|
x |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
C |
y |
15 |
40 |
35 |
20 |
25 |
15 |
10 |
25 |
25 |
5 |
10 |
40 |
20 |
40 |
40 |
10 |
40 |
10 |
|
z |
10 |
25 |
25 |
5 |
10 |
40 |
15 |
40 |
35 |
20 |
25 |
15 |
10 |
25 |
10 |
0 |
0 |
0 |
|
№ |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
75 |
А |
y |
25 |
5 |
10 |
40 |
15 |
40 |
35 |
20 |
25 |
15 |
15 |
30 |
45 |
15 |
10 |
5 |
0 |
25 |
|
z |
35 |
20 |
25 |
15 |
10 |
25 |
25 |
5 |
15 |
40 |
10 |
40 |
0 |
10 |
10 |
10 |
10 |
40 |
|
x |
50 |
50 |
55 |
45 |
55 |
45 |
50 |
50 |
55 |
45 |
35 |
50 |
40 |
40 |
20 |
25 |
10 |
10 |
B |
y |
40 |
40 |
40 |
40 |
40 |
50 |
5 |
40 |
5 |
10 |
45 |
10 |
10 |
45 |
0 |
0 |
10 |
40 |
|
z |
5 |
40 |
5 |
10 |
40 |
5 |
40 |
40 |
40 |
0 |
40 |
5 |
40 |
40 |
35 |
40 |
40 |
15 |
|
x |
20 |
15 |
15 |
15 |
15 |
20 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
15 |
10 |
10 |
20 |
35 |
C |
y |
0 |
10 |
15 |
25 |
10 |
25 |
40 |
10 |
20 |
40 |
20 |
45 |
20 |
45 |
40 |
25 |
30 |
0 |
|
z |
40 |
10 |
20 |
40 |
20 |
40 |
20 |
10 |
15 |
25 |
10 |
25 |
25 |
5 |
20 |
10 |
20 |
10 |
Задача 51. Определить величину двугранного угла между плоскостями P и Q.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
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 |
90 |
90 |
80 |
70 |
80 |
90 |
40 |
60 |
50 |
40 |
70 |
50 |
70 |
50 |
40 |
90 |
50 |
50 |
P1 |
y |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
30 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
30 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
40 |
60 |
50 |
40 |
70 |
50 |
90 |
90 |
80 |
70 |
80 |
90 |
20 |
10 |
70 |
40 |
70 |
30 |
P2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
30 |
40 |
30 |
40 |
30 |
40 |
30 |
40 |
30 |
40 |
30 |
40 |
30 |
40 |
30 |
40 |
30 |
40 |
|
x |
70 |
50 |
50 |
70 |
50 |
50 |
70 |
50 |
50 |
70 |
55 |
55 |
10 |
10 |
10 |
10 |
40 |
10 |
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 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
95 |
Q1 |
y |
40 |
30 |
30 |
35 |
40 |
40 |
40 |
30 |
30 |
40 |
35 |
30 |
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 |
45 |
70 |
80 |
40 |
85 |
55 |
90 |
95 |
90 |
95 |
90 |
35 |
35 |
30 |
30 |
70 |
10 |
25 |
Q2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
40 |
40 |
30 |
30 |
40 |
35 |
30 |
30 |
30 |
30 |
40 |
35 |
40 |
30 |
30 |
40 |
40 |
40 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
70 |
50 |
65 |
55 |
60 |
70 |
70 |
50 |
65 |
55 |
90 |
90 |
90 |
90 |
60 |
90 |
60 |
90 |
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 |
40 |
10 |
35 |
65 |
10 |
10 |
20 |
10 |
25 |
20 |
80 |
80 |
90 |
80 |
90 |
60 |
95 |
65 |
P1 |
y |
30 |
40 |
40 |
35 |
40 |
30 |
30 |
40 |
35 |
40 |
30 |
30 |
30 |
30 |
40 |
40 |
40 |
40 |
|
z |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
x |
20 |
80 |
25 |
20 |
75 |
60 |
40 |
80 |
35 |
65 |
30 |
40 |
40 |
30 |
30 |
65 |
25 |
55 |
P2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
30 |
30 |
35 |
40 |
40 |
40 |
30 |
30 |
40 |
35 |
35 |
40 |
40 |
30 |
40 |
40 |
40 |
40 |
|
x |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
50 |
40 |
40 |
40 |
10 |
10 |
45 |
10 |
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 |
70 |
50 |
50 |
65 |
30 |
30 |
40 |
50 |
40 |
20 |
95 |
95 |
95 |
95 |
40 |
30 |
10 |
30 |
Q1 |
y |
40 |
30 |
40 |
35 |
30 |
30 |
30 |
30 |
40 |
40 |
40 |
30 |
30 |
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 |
40 |
80 |
40 |
20 |
80 |
60 |
70 |
80 |
50 |
65 |
50 |
70 |
80 |
45 |
60 |
40 |
80 |
65 |
Q2 |
y |
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||||||||||||||||
|
z |
30 |
30 |
40 |
40 |
30 |
40 |
40 |
30 |
40 |
35 |
40 |
40 |
30 |
30 |
40 |
40 |
40 |
40 |
Задача 52. Дана пирамида SABC. Определить угол между гранями SAB и SBC.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
35 |
90 |
75 |
20 |
80 |
75 |
20 |
75 |
30 |
20 |
75 |
20 |
75 |
90 |
35 |
90 |
75 |
20 |
S |
y |
20 |
5 |
040 |
35 |
0 |
20 |
5 |
40 |
40 |
35 |
20 |
5 |
40 |
35 |
20 |
5 |
40 |
35 |
|
z |
40 |
35 |
20 |
5 |
40 |
40 |
35 |
20 |
0 |
5 |
40 |
35 |
20 |
5 |
45 |
35 |
20 |
5 |
|
x |
50 |
95 |
0 |
40 |
95 |
60 |
40 |
75 |
45 |
0 |
85 |
0 |
60 |
95 |
70 |
95 |
90 |
40 |
A |
y |
10 |
10 |
15 |
10 |
40 |
10 |
20 |
0 |
10 |
20 |
35 |
10 |
5 |
20 |
30 |
10 |
15 |
10 |
|
z |
5 |
20 |
5 |
20 |
10 |
5 |
10 |
35 |
35 |
10 |
0 |
20 |
10 |
10 |
0 |
20 |
5 |
20 |
|
x |
20 |
70 |
75 |
20 |
65 |
75 |
0 |
60 |
45 |
15 |
90 |
20 |
90 |
70 |
40 |
70 |
75 |
20 |
B |
y |
5 |
20 |
0 |
0 |
35 |
35 |
10 |
5 |
10 |
10 |
5 |
40 |
15 |
10 |
0 |
80 |
0 |
0 |
|
z |
15 |
10 |
35 |
40 |
15 |
0 |
20 |
10 |
40 |
20 |
15 |
0 |
5 |
20 |
0 |
10 |
35 |
40 |
|
x |
35 |
90 |
60 |
0 |
90 |
90 |
20 |
90 |
20 |
20 |
60 |
40 |
75 |
90 |
20 |
90 |
60 |
60 |
C |
y |
35 |
40 |
5 |
20 |
20 |
50 |
40 |
15 |
0 |
0 |
10 |
20 |
0 |
5 |
40 |
40 |
5 |
20 |
|
z |
0 |
0 |
10 |
10 |
0 |
15 |
0 |
5 |
20 |
40 |
5 |
10 |
35 |
40 |
0 |
0 |
10 |
10 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
35 |
90 |
35 |
90 |
35 |
20 |
30 |
75 |
20 |
35 |
90 |
80 |
35 |
90 |
90 |
35 |
90 |
35 |
S |
y |
40 |
35 |
20 |
5 |
40 |
35 |
0 |
20 |
5 |
40 |
35 |
40 |
20 |
5 |
35 |
20 |
5 |
40 |
|
z |
20 |
5 |
40 |
35 |
20 |
5 |
40 |
40 |
35 |
20 |
5 |
0 |
4 |
35 |
5 |
40 |
35 |
20 |
|
x |
50 |
90 |
20 |
70 |
35 |
20 |
45 |
90 |
50 |
20 |
70 |
95 |
35 |
90 |
90 |
20 |
70 |
35 |
A |
y |
5 |
0 |
5 |
20 |
0 |
0 |
35 |
5 |
40 |
15 |
10 |
10 |
35 |
40 |
0 |
5 |
20 |
0 |
|
z |
10 |
40 |
15 |
10 |
35 |
40 |
10 |
15 |
0 |
5 |
20 |
40 |
0 |
0 |
40 |
15 |
10 |
35 |
|
x |
35 |
70 |
35 |
90 |
20 |
0 |
20 |
60 |
40 |
50 |
95 |
90 |
50 |
95 |
70 |
35 |
90 |
20 |
B |
y |
0 |
10 |
35 |
40 |
15 |
20 |
20 |
10 |
20 |
5 |
20 |
0 |
10 |
10 |
10 |
35 |
40 |
15 |
|
z |
35 |
20 |
0 |
0 |
5 |
10 |
0 |
5 |
10 |
10 |
10 |
20 |
5 |
20 |
20 |
0 |
0 |
5 |
|
x |
20 |
95 |
50 |
95 |
50 |
40 |
15 |
75 |
0 |
35 |
90 |
65 |
20 |
70 |
95 |
50 |
95 |
50 |
C |
y |
15 |
20 |
10 |
10 |
5 |
10 |
40 |
35 |
40 |
0 |
0 |
10 |
5 |
20 |
20 |
10 |
10 |
5 |
|
z |
5 |
10 |
5 |
20 |
10 |
20 |
10 |
0 |
20 |
35 |
40 |
35 |
15 |
10 |
10 |
0 |
20 |
10 |
XI. Смешанные задачи
Все следующие задачи могут быть решены несколькими способами и включают в себя как решение определенных позиционных, так и метрических задач. Решите эти задачи несколькими способами.
Задача 53. Определить расстояние от точки C до прямой общего положения AB.
|
№ |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
65 |
60 |
40 |
60 |
70 |
65 |
70 |
60 |
70 |
70 |
60 |
70 |
70 |
60 |
40 |
60 |
65 |
55 |
А |
y |
0 |
0 |
0 |
0 |
40 |
45 |
40 |
40 |
25 |
35 |
0 |
0 |
40 |
35 |
40 |
10 |
40 |
40 |
|
z |
5 |
40 |
10 |
0 |
40 |
0 |
40 |
10 |
40 |
40 |
10 |
40 |
40 |
0 |
10 |
5 |
5 |
40 |
|
x |
20 |
30 |
20 |
20 |
30 |
20 |
25 |
30 |
50 |
30 |
20 |
25 |
25 |
30 |
25 |
25 |
40 |
20 |
B |
y |
40 |
40 |
25 |
35 |
0 |
0 |
0 |
0 |
0 |
0 |
40 |
45 |
5 |
10 |
5 |
40 |
10 |
5 |
|
z |
40 |
10 |
40 |
40 |
10 |
40 |
5 |
40 |
10 |
0 |
40 |
0 |
0 |
40 |
40 |
40 |
40 |
10 |
|
x |
60 |
15 |
70 |
65 |
20 |
25 |
30 |
75 |
20 |
25 |
70 |
65 |
30 |
15 |
60 |
10 |
20 |
70 |
C |
y |
40 |
5 |
35 |
35 |
40 |
40 |
40 |
5 |
35 |
35 |
40 |
40 |
35 |
35 |
10 |
5 |
35 |
10 |
|
z |
35 |
35 |
35 |
40 |
40 |
0 |
35 |
35 |
35 |
40 |
40 |
0 |
40 |
5 |
25 |
10 |
10 |
5 |
|
№ |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
40 |
60 |
30 |
65 |
65 |
60 |
70 |
70 |
60 |
70 |
55 |
65 |
60 |
40 |
45 |
45 |
60 |
40 |
А |
y |
10 |
0 |
10 |
0 |
5 |
10 |
40 |
40 |
10 |
40 |
40 |
40 |
10 |
40 |
15 |
35 |
0 |
0 |
|
z |
0 |
0 |
0 |
45 |
0 |
40 |
25 |
35 |
0 |
0 |
40 |
5 |
5 |
10 |
30 |
5 |
40 |
10 |
|
x |
20 |
20 |
70 |
20 |
20 |
30 |
50 |
30 |
20 |
25 |
20 |
40 |
25 |
15 |
10 |
35 |
30 |
20 |
B |
y |
40 |
40 |
40 |
40 |
40 |
40 |
10 |
0 |
40 |
0 |
5 |
10 |
40 |
5 |
5 |
0 |
40 |
25 |
|
z |
25 |
35 |
40 |
0 |
40 |
0 |
0 |
0 |
40 |
45 |
10 |
40 |
40 |
40 |
35 |
10 |
10 |
40 |
|
x |
70 |
65 |
20 |
25 |
60 |
75 |
20 |
25 |
70 |
65 |
70 |
20 |
10 |
60 |
80 |
10 |
15 |
70 |
C |
y |
35 |
40 |
40 |
0 |
35 |
35 |
35 |
40 |
40 |
0 |
10 |
35 |
5 |
10 |
10 |
30 |
5 |
35 |
|
z |
35 |
35 |
40 |
40 |
40 |
5 |
35 |
35 |
40 |
40 |
5 |
10 |
10 |
35 |
20 |
40 |
35 |
35 |
Задача 54. Определить расстояние от точки E до плоскости ABC.
№ |
|
1 |
2 |
3 |
4 |
5 |
|
6 |
7 |
|
8 |
9 |
|
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
||
|
x |
45 |
45 |
30 |
45 |
45 |
45 |
45 |
50 |
50 |
85 |
85 |
85 |
85 |
85 |
55 |
50 |
50 |
45 |
|||||
A |
y |
40 |
0 |
40 |
30 |
10 |
15 |
30 |
10 |
5 |
|
30 |
10 |
0 |
|
40 |
10 |
10 |
35 |
0 |
0 |
|||
|
z |
40 |
20 |
0 |
40 |
20 |
10 |
0 |
|
15 |
20 |
15 |
40 |
20 |
20 |
40 |
30 |
10 |
40 |
10 |
||||
|
x |
5 |
5 |
45 |
5 |
5 |
|
15 |
30 |
30 |
10 |
45 |
45 |
45 |
65 |
45 |
10 |
25 |
10 |
25 |
||||
B |
y |
30 |
10 |
10 |
40 |
10 |
10 |
0 |
|
40 |
10 |
40 |
0 |
40 |
10 |
10 |
0 |
0 |
15 |
35 |
||||
|
z |
15 |
40 |
40 |
20 |
40 |
40 |
40 |
40 |
40 |
40 |
20 |
40 |
0 |
20 |
25 |
35 |
10 |
35 |
|||||
|
x |
0 |
40 |
0 |
10 |
40 |
40 |
35 |
15 |
40 |
0 |
|
40 |
40 |
30 |
40 |
35 |
20 |
35 |
15 |
||||
C |
y |
0 |
40 |
0 |
10 |
40 |
40 |
35 |
15 |
40 |
0 |
|
40 |
40 |
30 |
40 |
35 |
20 |
35 |
15 |
||||
|
z |
0 |
0 |
20 |
0 |
0 |
|
0 |
15 |
0 |
5 |
|
0 |
|
0 |
0 |
|
40 |
0 |
0 |
0 |
0 |
0 |
|
|
x |
10 |
5 |
45 |
5 |
10 |
35 |
15 |
15 |
10 |
80 |
85 |
45 |
85 |
80 |
20 |
15 |
25 |
35 |
|||||
E y |
0 0 |
0 |
0 |
0 |
40 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 35 |
40 |
40 |
35 |
||||||||
|
z |
40 |
10 |
0 |
40 |
0 |
|
40 |
5 |
|
40 |
0 |
|
40 |
10 |
0 |
|
40 |
0 |
40 |
35 |
40 |
0 |
|
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|||||
|
x |
85 |
85 |
80 |
80 |
45 |
45 |
45 |
45 |
5 |
|
45 |
55 |
60 |
40 |
55 |
50 |
45 |
50 |
50 |
||||
A |
y |
40 |
35 |
15 |
10 |
45 |
20 |
40 |
40 |
40 |
10 |
45 |
0 |
|
40 |
30 |
35 |
10 |
0 |
20 |
||||
|
z |
0 |
15 |
0 |
40 |
40 |
0 |
10 |
30 |
10 |
15 |
40 |
20 |
0 |
40 |
10 |
20 |
25 |
0 |
|||||
|
x |
75 |
60 |
60 |
40 |
30 |
15 |
30 |
25 |
25 |
5 |
|
15 |
20 |
55 |
15 |
35 |
10 |
5 |
35 |
||||
B |
y |
10 |
0 |
40 |
5 |
0 |
|
0 |
0 |
|
0 |
0 |
|
0 |
|
30 |
10 |
10 |
40 |
0 |
10 |
10 |
0 |
|
|
z |
40 |
40 |
40 |
20 |
0 |
|
40 |
40 |
10 |
40 |
40 |
15 |
40 |
40 |
20 |
35 |
35 |
35 |
35 |
||||
|
x |
45 |
45 |
40 |
70 |
5 |
|
5 |
5 |
|
5 |
45 |
15 |
40 |
30 |
15 |
35 |
10 |
25 |
35 |
10 |
|||
C |
y |
15 |
30 |
10 |
40 |
15 |
40 |
20 |
20 |
20 |
40 |
0 |
40 |
0 |
10 |
20 |
35 |
35 |
35 |
|||||
|
z |
10 |
0 |
15 |
5 |
30 |
10 |
0 |
|
40 |
10 |
10 |
0 |
0 |
|
20 |
0 |
0 |
0 |
0 |
10 |
|||
|
x |
55 |
85 |
75 |
80 |
10 |
5 |
45 |
5 |
10 |
35 |
20 |
15 |
15 |
20 |
25 |
15 |
40 |
45 |
|||||
E |
y |
40 |
0 |
0 |
0 |
40 |
10 |
0 |
|
40 |
0 |
|
40 |
0 |
0 |
|
40 |
0 |
35 |
0 |
35 |
40 |
||
|
z |
40 |
5 |
40 |
0 |
0 |
|
0 |
0 |
|
0 |
0 |
|
40 |
40 |
10 |
40 |
40 |
35 |
0 |
40 |
35 |
Задача 55. Определить расстояние от точки E до плоскости ABC.
|
№ |
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 |
E |
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 |
45 |
45 |
30 |
45 |
45 |
45 |
45 |
50 |
50 |
85 |
85 |
85 |
85 |
85 |
85 |
55 |
50 |
50 |
A |
y |
40 |
0 |
40 |
30 |
10 |
15 |
30 |
10 |
5 |
30 |
10 |
0 |
40 |
10 |
10 |
35 |
0 |
0 |
|
z |
40 |
20 |
0 |
40 |
20 |
10 |
0 |
15 |
20 |
15 |
40 |
20 |
20 |
40 |
30 |
10 |
40 |
10 |
|
x |
5 |
5 |
45 |
5 |
5 |
15 |
30 |
30 |
10 |
45 |
45 |
45 |
65 |
45 |
10 |
25 |
10 |
25 |
B |
y |
30 |
10 |
10 |
40 |
10 |
10 |
0 |
40 |
10 |
40 |
0 |
40 |
10 |
10 |
0 |
0 |
15 |
35 |
|
z |
15 |
40 |
40 |
20 |
40 |
40 |
40 |
40 |
40 |
40 |
40 |
20 |
40 |
0 |
20 |
25 |
10 |
35 |
|
x |
30 |
15 |
5 |
25 |
25 |
5 |
5 |
10 |
20 |
60 |
75 |
60 |
45 |
65 |
25 |
10 |
40 |
10 |
C |
y |
0 |
40 |
0 |
10 |
40 |
40 |
35 |
15 |
40 |
0 |
40 |
40 |
30 |
40 |
35 |
20 |
35 |
15 |
|
z |
0 |
0 |
20 |
0 |
0 |
0 |
15 |
0 |
5 |
0 |
0 |
0 |
40 |
0 |
0 |
0 |
0 |
0 |
|
№ |
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 |
E |
y |
35 |
0 |
35 |
0 |
40 |
35 |
35 |
0 |
35 |
0 |
25 |
40 |
25 |
40 |
40 |
40 |
25 |
35 |
|
z |
40 |
35 |
35 |
0 |
35 |
40 |
40 |
35 |
35 |
0 |
40 |
25 |
40 |
25 |
20 |
25 |
40 |
40 |
|
x |
85 |
85 |
80 |
80 |
45 |
45 |
45 |
45 |
5 |
45 |
55 |
65 |
40 |
55 |
50 |
45 |
50 |
50 |
A |
y |
40 |
35 |
15 |
10 |
40 |
20 |
40 |
40 |
40 |
10 |
40 |
0 |
40 |
30 |
35 |
10 |
0 |
20 |
|
z |
0 |
15 |
0 |
40 |
40 |
0 |
10 |
30 |
10 |
15 |
40 |
20 |
0 |
40 |
10 |
20 |
25 |
0 |
|
x |
75 |
30 |
30 |
40 |
30 |
15 |
30 |
25 |
25 |
5 |
15 |
20 |
55 |
15 |
35 |
10 |
5 |
35 |
B |
y |
10 |
0 |
40 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
30 |
10 |
10 |
40 |
0 |
10 |
10 |
0 |
|
z |
40 |
40 |
40 |
20 |
0 |
40 |
40 |
10 |
40 |
40 |
15 |
40 |
40 |
20 |
35 |
35 |
35 |
35 |
|
x |
15 |
30 |
10 |
40 |
15 |
40 |
20 |
20 |
20 |
40 |
0 |
40 |
0 |
10 |
20 |
35 |
35 |
35 |
C |
y |
15 |
30 |
10 |
40 |
15 |
40 |
10 |
10 |
10 |
40 |
0 |
40 |
0 |
10 |
20 |
35 |
35 |
35 |
|
z |
10 |
0 |
15 |
5 |
30 |
10 |
0 |
40 |
10 |
10 |
0 |
0 |
20 |
0 |
0 |
0 |
10 |
10 |
Задача 56. Определить расстояние от точки M до 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 |
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 |
40 |
35 |
60 |
35 |
60 |
10 |
40 |
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 |
40 |
40 |
25 |
25 |
10 |
10 |
60 |
45 |
55 |
60 |
60 |
60 |
35 |
50 |
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 |
35 |
|
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 |
60 |
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 |
Задача 57. На прямой AB найти точку M, удаленную от плоскости CDE на 20 мм.
№ |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
|
x |
90 |
60 |
50 |
80 |
25 |
65 |
90 |
60 |
50 |
80 |
25 |
65 |
55 |
55 |
80 |
45 |
80 |
45 |
A |
y |
0 |
0 |
40 |
10 |
15 |
35 |
5 |
40 |
15 |
25 |
20 |
40 |
5 |
25 |
35 |
40 |
20 |
45 |
|
z |
5 |
40 |
15 |
25 |
20 |
40 |
0 |
10 |
40 |
10 |
15 |
35 |
35 |
25 |
20 |
45 |
35 |
40 |
|
x |
35 |
50 |
10 |
40 |
0 |
35 |
35 |
50 |
10 |
40 |
0 |
35 |
25 |
0 |
45 |
10 |
45 |
10 |
B |
y |
25 |
40 |
30 |
40 |
0 |
5 |
25 |
30 |
10 |
0 |
40 |
35 |
35 |
5 |
40 |
35 |
45 |
20 |
|
z |
25 |
30 |
10 |
0 |
40 |
35 |
25 |
40 |
30 |
40 |
0 |
0 |
40 |
0 |
45 |
20 |
40 |
35 |
|
x |
45 |
85 |
45 |
85 |
50 |
85 |
45 |
85 |
45 |
85 |
50 |
85 |
45 |
85 |
85 |
45 |
85 |
45 |
C |
y |
0 |
35 |
20 |
10 |
30 |
20 |
35 |
10 |
35 |
0 |
35 |
30 |
35 |
20 |
15 |
5 |
35 |
25 |
|
z |
35 |
10 |
35 |
0 |
35 |
30 |
0 |
35 |
20 |
10 |
30 |
10 |
20 |
10 |
35 |
25 |
15 |
0 |
|
x |
5 |
70 |
5 |
75 |
10 |
45 |
20 |
40 |
5 |
75 |
10 |
45 |
5 |
70 |
45 |
5 |
70 |
20 |
D |
y |
10 |
0 |
30 |
35 |
25 |
35 |
0 |
10 |
25 |
35 |
20 |
25 |
20 |
0 |
5 |
15 |
5 |
5 |
|
z |
20 |
35 |
25 |
35 |
20 |
20 |
35 |
20 |
30 |
35 |
25 |
35 |
30 |
35 |
25 |
35 |
40 |
40 |
|
x |
20 |
50 |
30 |
50 |
35 |
65 |
5 |
20 |
30 |
50 |
35 |
65 |
25 |
45 |
70 |
20 |
45 |
5 |
E |
y |
35 |
20 |
0 |
5 |
0 |
0 |
20 |
35 |
10 |
15 |
0 |
5 |
0 |
35 |
40 |
40 |
25 |
35 |
|
z |
0 |
10 |
10 |
15 |
0 |
5 |
10 |
0 |
0 |
5 |
0 |
0 |
5 |
0 |
5 |
5 |
5 |
15 |
№ |
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
|
x |
40 |
80 |
50 |
90 |
55 |
55 |
40 |
80 |
60 |
90 |
45 |
80 |
45 |
80 |
80 |
50 |
60 |
90 |
A |
y |
30 |
10 |
0 |
40 |
35 |
25 |
40 |
30 |
40 |
0 |
45 |
20 |
45 |
35 |
40 |
40 |
0 |
0 |
|
z |
40 |
30 |
40 |
0 |
5 |
25 |
30 |
10 |
0 |
40 |
40 |
35 |
40 |
20 |
25 |
15 |
40 |
5 |
|
x |
30 |
40 |
10 |
65 |
25 |
0 |
30 |
40 |
10 |
65 |
10 |
45 |
10 |
45 |
10 |
45 |
50 |
35 |
B |
y |
40 |
15 |
25 |
20 |
40 |
0 |
0 |
40 |
10 |
15 |
20 |
45 |
35 |
40 |
40 |
30 |
40 |
25 |
|
z |
0 |
40 |
10 |
15 |
35 |
5 |
40 |
15 |
25 |
20 |
35 |
40 |
20 |
45 |
0 |
10 |
30 |
25 |
|
x |
40 |
85 |
40 |
80 |
45 |
85 |
40 |
85 |
45 |
80 |
45 |
85 |
45 |
85 |
40 |
40 |
85 |
85 |
C |
y |
10 |
25 |
15 |
20 |
20 |
10 |
30 |
30 |
5 |
25 |
25 |
30 |
5 |
15 |
10 |
20 |
35 |
0 |
|
z |
20 |
30 |
5 |
25 |
35 |
20 |
10 |
25 |
15 |
20 |
5 |
15 |
25 |
35 |
0 |
35 |
10 |
35 |
|
x |
5 |
45 |
15 |
40 |
5 |
45 |
45 |
45 |
15 |
40 |
20 |
70 |
5 |
45 |
75 |
5 |
70 |
5 |
D |
y |
10 |
35 |
35 |
35 |
30 |
0 |
0 |
20 |
35 |
30 |
5 |
5 |
15 |
5 |
35 |
30 |
0 |
10 |
|
z |
35 |
20 |
35 |
30 |
20 |
35 |
35 |
35 |
35 |
35 |
40 |
40 |
35 |
25 |
35 |
25 |
35 |
20 |
|
x |
20 |
60 |
5 |
55 |
25 |
70 |
5 |
60 |
5 |
55 |
5 |
45 |
20 |
70 |
50 |
30 |
50 |
20 |
E |
y |
35 |
10 |
0 |
0 |
5 |
35 |
35 |
0 |
10 |
0 |
35 |
25 |
40 |
40 |
5 |
0 |
20 |
35 |
|
z |
0 |
0 |
10 |
0 |
0 |
0 |
10 |
10 |
0 |
0 |
15 |
5 |
5 |
5 |
15 |
10 |
10 |
0 |