, ( ).
. P (x, y, z) ( ) 1´4 . (x1, y1 , z1) (x 2 , y2 , z2) 2´4 . M ´4 ( M ), : . 4´4 . . h ≠ 1 h ≠ 0, h, .. , x* = x¢/h, y* = y¢/h, z* = z¢/h. h ( ) , , , (x¢, y¢, z¢).
2.
:
: , .
1. , . 2. ( ).
2. , [2]:
a) x z, ;
b) xz (y = 0);
c) x;
d) x z;
e) 90 z;
f) f y.
3´3 .
3. y z, .
1´3 .
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4. .
. 3´1 .
5. .
1´1 .
6. f , y , , : x = l, z = n; :
a) , , , y;
b) y;
c) ( /. a) .
7. , . . , .
8. χ , (0, 0, 0) , ; :
a) , , , - ;
b) , /. a ;
c) ( /. a) .
9. , :
a) - , , , ;
b) , - ;
c) , /. b ;
d) ( /. b) ( );
e) ( /. a) .
6, 7, 8 9 .
10. xy (z = 0), - , , .
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2.
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3 1 | |
x1 = 100; y1 = 100; z1 = 50; x2 = 0; y2 = 100; z2 = 150; x3 = 100; y3 = 0; z3 = 150; x4 = 100; y4 = 100; z4 = 150 | |
/ | |
2a | a = 3; j = 1.5* |
2d | g = 1.5* |
2f | f = 30 |
m = 100; n = 150* | |
p = 0.03; q = 0.02* | |
s = 2* | |
f = 50; l = 100; n = 50* | |
χ = 105 | |
D = -50 | |
* , (. 1) |
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3 2 | |
x1 = 200; y1 = 100; z1= 200; x2 = 200; y2 = 250; z2= 100; x3 = 100; y3 = 250; z3= 200; x4 = 200; y4 = 250; z4 = 200 | |
/ | |
2a | a = 0.5; j = 1.5 * |
2d | g = -0.5* |
2f | f = 120 |
m = 150; n = 100 * | |
p = 0.003; r = 0.001 * | |
s = 0.5* | |
f = 140; l = 100; n = 100* | |
χ = 80 | |
D = 100 | |
* , (. 1) | |
: | |
3 3 | |
x1 = 100; y1 = 250; z1= 50; x2 = 100; y2 = 250; z2= 250; x3 = 200; y3 = 150; z3= 150; x4 = 200; y4 = 250; z4 = 150 | |
/ | |
2a | a = 2.1; j = 1.2* |
2d | g = 1.3* |
2f | f = 45 |
m = 50; n = 300 * | |
q = 0.01; r = 0.02* | |
s = 3* | |
f = 80; l = 300; n = 150* | |
χ = 100 | |
D = 200 | |
* , (. 1) |
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3 4 | |
x1 = 100; y1 = 150; z1= 300; x2 = 200; y2 = 150; z2= 200; x3 = 100; y3 = 50; z3= 200; x4 = 100; y4 = 150; z4 = 200 | |
/ | |
2a | a = 1.6; j = 1.2* |
2d | g = 1.1* |
2f | f = 90 |
m = 50; n = -100* | |
p =0.002; q = 0.001; r = 0.003* | |
s = 0.6 * | |
f = 115; l = 150; n = 150* | |
χ = 130 | |
D = -150 | |
* , (. 1) | |
: | |
3 5 | |
x1 = -200; y1 = -200; z1= 0; x2 = -100; y2 = -200; z2= 100; x3 = -200; y3 = -100; z3= 100; x4 = -200; y4 = -200; z4 = 100 | |
/ | |
2a | a = 0.5; j = 0.8* |
2d | g = 1.2* |
2f | f = 30 |
m = 300; n = 100* | |
q = 0.002* | |
s = 1.5* | |
f = 15; l = 200; n = 100* | |
χ = 160 | |
D = -200 | |
* , (. 1) |
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3 6 | |
x1 = -100; y1 = -100; z1= -300; x2 = +200; y2 = -100; z2= -200; x3 = -100; y3 = -200; z3= -200; x4 = -100; y4 = -100; z4 = -200 | |
/ | |
2a | a = 0.4; j = 1.3* |
2d | g = 0.5* |
2f | f = 60 |
m = 300; n = 400* | |
r = 0.008* | |
s = 1.8* | |
f = 250; l = -400; n = -300* | |
χ = 210 | |
D = 130 | |
* , (. 1) |
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