2086
.pdf1.10. Проекции плоскости. Классификация плоскостей (рис. 1.14)
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
|
|
В2 |
|
|
|
|
В2 |
|||
А |
|
|
|
С2 |
|
|
|
|||
|
|
|
|
|
|
|
|
С |
||
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
||
2 |
|
|
В |
1 |
А2 |
|
2 |
|||
А |
|
|
|
|
|
С |
||||
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
||
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
А |
|
1 |
|||
|
|
|
|
С1 |
1 |
|
|
В1 |
||
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
Рис. 1.14
1.11. Плоскости частного положения
________________________________________________________________
________________________________________________________________
Проецирующие плоскости (рис. 1.15, рис. 1.16, рис. 1.17)___________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
Рис. 1.15
11
Рис. 1.16
Рис. 1.17
Плоскости уровня (рис. 1.18) ________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
|
|
|
|
|
A2 |
|
D2 |
|
|
|
|
|
f |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
||||
A |
B |
C |
|
|
a2 |
=b2 |
|
|
o |
b3 |
|||||
|
2 |
2 |
|
2 |
|
|
|
|
|
|
|
|
|
a3 |
|
|
|
B1 |
|
C2 |
|
|
B2 |
x |
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
a1 =b1 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|||||
A1 |
|
|
C1 |
A1 =C1 |
B1 =D1 |
ho |
|
||||||||
|
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
а) |
|
|
|
|
б) |
|
|
|
|
|
|
|
в) |
|
|
|
|
|
|
|
|
Рис. 1.18 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
|
|
|
|
|
|
|
|
Лекция 2
АКСОНОМЕТРИЧЕСКИЕ ПРОЕКЦИИ. ОБЩИЕ СВЕДЕНИЯ
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
|
|
|
|
s |
|
|
|
__________________ |
|
|
|
- |
|
|
|
__________________ |
|
|
|
|
|
Z |
|
|
__________________ |
|
|
|
|
П |
|
|
|
||
|
|
|
|
|
|
|
|
__________________ |
|
|
|
|
|
А |
|
|
_________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Z- |
|
|
|
|
|
|
__________________ |
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|||
- |
|
|
|
|
|
е |
|
__________________ |
А |
|
|
|
|
|
|
__________________ |
|
|
|
|
|
|
|
z |
|
|
|
|
|
|
|
|
Oе |
|
|
|
е |
- |
|
|
е |
|
__________________ |
|
|
|
А |
у |
|
__________________ |
|||
|
z |
|
х |
|
|
|||
е- |
O |
- |
|
х |
|
|
|
|
|
|
А |
|
|
__________________ |
|||
|
|
|
|
|
||||
х |
|
|
|
X |
|
|
||
А- |
е- |
|
|
1 |
|
y |
__________________ |
|
х |
|
|
|
|
|
|
||
X- |
у |
|
|
|
|
|
|
__________________ |
|
|
|
|
|
|
|
||
А- |
|
|
y- |
|
|
|
|
__________________ |
1 |
|
|
|
|
|
|
__________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
__________________ |
|
|
|
|
|
|
|
|
__________________ |
|
|
|
|
|
|
|
|
___________________ |
|
|
|
Рис. 2.1 |
|
|
|
|
___________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
13 |
|
|
|
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
A2 |
|
|
|
z |
|
|
z |
|
|
|
|
|
|||||
|
|
|
|
|
||||
|
|
|
|
|
||||
x |
|
|
|
|
o |
|
|
|
|
|
|
|
|
|
o |
||
|
|
|
|
|
|
|
||
|
A1 |
|
|
|
y |
x |
|
y |
|
|
|
||||||
|
|
|
|
|
|
|
||
|
|
|
а) |
|
|
Рис. 2.2 |
|
б) |
|
|
|
|
|
|
|
|
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
14
2.1. Стандартные аксонометрические проекции |
|
|
|||||||||||||||||||||
ГОСТ 2.317-69 «Аксонометрические проекции» предусматривает |
|||||||||||||||||||||||
применение в инженерной графике двух прямоугольных и трех косоугольных |
|||||||||||||||||||||||
аксонометрий: прямоугольной изометрии; прямоугольной диметрии; |
|||||||||||||||||||||||
косоугольной фронтальной и горизонтальной изометрии; косоугольной |
|||||||||||||||||||||||
фронтальной диметрии. Углы между осями и коэффициенты искажения в |
|||||||||||||||||||||||
аксонометрии приведены в таблице. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
Название |
|
Расположение осей |
|
|
Коэффициенты |
||||||||||||||||||
|
|
|
|
|
|
|
|
|
w |
z , |
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
Прямоугольная |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
u = v = w = 0,82 |
|||
|
|
|
1 |
2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
изометрическая |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
, |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
, |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
проекция |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
U = V = W = 1,0 |
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
y |
|
|
|||||
|
|
x |
u |
|
|
|
|
|
0 |
|
|
|
v |
|
|
|
|||||||
|
|
|
|
|
|
3 |
|
|
|
|
|
|
|
|
|||||||||
|
|
|
|
|
|
|
|
w |
z |
|
, |
|
|
|
|
|
|
|
|
|
|
||
|
|
|
' |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
0 |
|
|
|
|
|
|
|
|
|
9 |
|
|
|
|
|
|
|
|||
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
u = w = 0,94 |
||||
|
|
|
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|||||||
Прямоугольная |
|
7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
x , |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
v = 0,47 |
|
диметрическая |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
' |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
проекция |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
|
|
|
|
u |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
|
|
U = W = 1,0 |
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
y |
, |
V = 0,5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
v |
|
|||
|
|
|
w z , |
|
|
|
|
|
|
|
|
|
|
|
|||||||||
Косоугольная |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
, |
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
фронтальная |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
x |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
U = V = W = 1,0 |
||||
изометрия |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
u |
|
|
|
|
|
|
|
|
|
|
|
(30 , 60 ) |
|
|||||||||
|
|
|
|
|
|
|
|
|
5 |
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
4 |
|
|
y |
|
|
, |
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
v |
|
|
|
|
|
|
|
|
|
||||
|
|
|
w |
|
|
|
z |
, |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
Косоугольная |
|
|
|
|
|
|
|
|
9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
горизонтальная |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
U = V = W = 1,0 |
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
изометрия |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(45 , 60 ) |
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
x , |
|
|
|
|
|
|
|
|
|
3 |
|
|
|
|
|
y , |
|
|
|
||
|
|
u |
|
|
90 |
|
v |
|
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
w |
z , |
|
|
|
|
|
|
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
9 |
|
|
|
|
|
|
|
|
|
|
||
Косоугольная |
|
|
|
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
U = W = 1,0 |
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
фронтальная |
|
, |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
V = 0,5 |
||
|
x |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
диметрия |
|
u |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(30 , 60 ) |
||||
|
|
|
|
|
|
|
|
|
|
|
|
5 |
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
|
|
, |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
v |
|
|
y |
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
15 |
|
|
|
|
|
|
|
|
|
|
|
2.2. Построение окружностей в изометрии |
||
|
|
___________________________________ |
z |
|
___________________________________ |
|
|
___________________________________ |
|
|
___________________________________ |
|
|
___________________________________ |
|
|
___________________________________ |
|
|
___________________________________ |
|
|
___________________________________ |
x |
y |
___________________________________ |
___________________________________ |
||
|
|
__________________________________ |
|
|
___________________________________ |
Рис. 2.3 |
|
_____________________________________________ |
________________________________________________________________
2.3. Построение овалов в изометрии (рис. 2.4)
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
а) |
б) |
в) |
г) |
д) |
Рис. 2.4
16
2.4. Штриховка в изометрии (рис. 2.5) |
|
|
|
|
|
|
|
|
|
z |
|||||||||
|
|
|
|
|
|
|
|
|
|||||||||||
_______________________________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
_______________________________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
_______________________________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
_______________________________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
_______________________________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
_______________________________________ x |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
y |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
______________________________________ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
__________________________________________ |
|
|
|
|
Рис. 2.5 |
||||||||||||||
|
|
|
|
|
2.5. Построение шестигранника в изометрии (рис. 2.7, рис. 2.7)
Z
X
X
h
O2 5 6
1 |
|
O1 |
2 |
|
|
||||
|
|
|
||
3 |
Y |
|
4 |
Рис. 2.6
17
Рис. 2.7
18
Лекция 3
ВЗАИМНОЕ ПОЛОЖЕНИЕ ПРЯМОЙ И ПЛОСКОСТИ. ВЗАИМНОЕ ПОЛОЖЕНИЕ ДВУХ ПЛОСКОСТЕЙ
3.1. Взаимное расположение прямых
a2 |
|
|
Параллельный прямые (рис. 3.1)____________________ |
|||||||||||||||||
|
__________________________________________ |
|||||||||||||||||||
|
||||||||||||||||||||
|
|
b2 |
|
|
|
|||||||||||||||
|
|
|
|
__________________________________________ |
||||||||||||||||
|
|
|
||||||||||||||||||
|
|
|
|
|
|
|
||||||||||||||
a1 |
|
b1 |
|
|
__________________________________________ |
|||||||||||||||
|
|
|||||||||||||||||||
|
||||||||||||||||||||
|
|
|
|
|
|
|
__________________________________________ |
|||||||||||||
|
|
|
|
|
|
|
__________________________________________ |
|||||||||||||
|
|
|
|
|
|
|
||||||||||||||
|
|
|
|
|
|
|
__________________________________________________ |
|||||||||||||
|
|
Рис. 3.1 |
|
|
|
Пересекающиеся прямые (рис. 3.2) – _______________ |
||||||||||||||
|
с |
|
b2 |
|||||||||||||||||
|
2 |
|
|
|
|
|
____________________________________________ |
|
||||||||||||
|
|
|
|
|
|
|||||||||||||||
a |
|
|
|
|
|
|
|
|
d2 |
____________________________________________ |
|
|||||||||
2 |
|
|
|
|
|
|
|
|
|
____________________________________________ |
|
|||||||||
|
|
|
|
|
|
|
|
|
|
|
||||||||||
a1 |
|
|
|
|
|
|
|
|
|
____________________________________________ |
|
|||||||||
|
|
|
|
|
|
|
|
|
|
|||||||||||
|
|
|
|
|
|
|
|
b1 |
____________________________________________ |
|
||||||||||
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
Рис. 3.2 |
|
____________________________________________ |
|
||||||||||||||
|
|
|
|
|
||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
Скрещивающиеся прямые (рис. 3.3) |
|
|
|
|
|
|
|
|
|
|
||||||||||
_________________________________________________________ |
|
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|
|
|||||||||||
_________________________________________ |
k |
|
|
|
|
|
|
|
||||||||||||
_________________________________________ |
2 |
|
|
|
|
|
|
|||||||||||||
|
|
|
|
|
||||||||||||||||
|
|
|
|
|
|
|
|
|||||||||||||
_________________________________________ |
l2 |
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
||||||||||||||||
____________________________________________ |
|
|
|
|
|
|
||||||||||||||
|
|
|
|
|
|
|||||||||||||||
____________________________________________ |
|
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|
|
|||||||||||
_________________________________________ |
k |
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|||||||||||||
_________________________________________ |
1 |
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|||||||||||||
________________________________________ |
|
|
|
|
|
|
|
|
|
|||||||||||
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|||||||||||||
|
|
|
|
|
|
|
||||||||||||||
_________________________________________ |
l |
|
|
|
|
|
|
|
|
|||||||||||
_________________________________________ |
1 |
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|
|
|||||||||||
_________________________________________ |
|
|
|
|
|
|
|
|
|
|
||||||||||
_________________________________________ |
|
|
|
|
|
|
|
|
|
|
||||||||||
_________________________________________ |
|
|
|
Рис. 3.3 |
|
|
|
|
_________________________________________
________________________________________________________________
________________________________________________________________
19
3.2. Проекции прямого плоского угла. Теорема о прямом угле (рис. 3.4)
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
|
A2 |
|
C |
|
|
|
|
|
|
|
E2 |
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|||||
|
|
|
|
2 |
C2 |
. |
|
|||||
|
B . |
|
|
|
|
|||||||
|
|
|
|
|
||||||||
|
|
|
|
D2 |
|
|
||||||
2 |
|
|
|
|
|
|
D |
|||||
|
|
|
|
|
|
|
|
|
|
|
||
|
B1 |
|
|
C1 |
C1 |
|
|
|
. 1 |
|
E1 |
|
|
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|||||||
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|||
A1 |
а) |
|
|
|
б) |
|||||||
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
Рис. 3.4
3.3. Построение точки пересечения прямой и плоскости (рис. 3.5)
_____________________________________________________
_____________________________________________________
|
|
|
|
|
B2 |
|
|
|
|
|
______________________ |
|
|
|
|
|
|
|
______________________ |
||||
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
M |
______________________ |
|
|
|
|
|
|
|
|
|
|
||
A |
|
|
|
2 |
______________________ |
||||||
2 |
|
L |
|
|
|
|
|
|
______________________ |
||
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
______________________ |
|||
2 |
|
|
|
|
|
C2 |
______________________ |
||||
|
|||||||||||
|
|||||||||||
A1 |
|
|
|
|
|
|
|
|
______________________ |
||
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
______________________ |
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
M1 |
______________________ |
|
|
|
|
|
|
|
|
|
|
||
L |
|
|
|
|
|
C1 |
______________________ |
||||
|
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
______________________ |
|||
1 |
|
|
|
|
|
|
|
|
______________________ |
||
|
|
|
|
|
|
|
B1 |
______________________ |
|||
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
______________________ |
||||
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Рис. 3.5 |
|
20