Задача № 6
Даны координаты точек: A1(x1 ; y1 ; z1), A2(x2 ; y2 ; z2), A3(x3 ; y3 ; z3), A4(x4 ; y4 ; z4).
Требуется: 1) написать канонические уравнения прямых A1A2 и A1A4 и найти угол между ними; 2) написать общее уравнение плоскости A1A2A3 ; 3) найти угол между прямой A1A4 и плоскостью A1A2A3 ; 4) написать канонические уравнения высоты, опущенной из вершины A4 на грань A1A2A3 ; 5) найти координаты проекции точки A4 на грань A1A2A3 .
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1 |
(2; 3; 2) |
(10; 7; 3) |
(6; 6; 3) |
(8; 9; 5) |
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2 |
(3; 5; 2) |
(1; 7; 5) |
(5; 6; 8) |
(1; 6; 4) |
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3 |
(6; 1; 4) |
(3;-3; 8) |
(5;-5; 8) |
(8; 3; 3) |
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4 |
(2; 5; 4) |
(5; 3; 6) |
(8; 3; 5) |
(8; 2; 10) |
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5 |
(3; 4; 3) |
(7;-4; 4) |
(6; 0; 4) |
(9; 10; 6) |
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6 |
(1; 2; 3) |
(3; 4; 6) |
(-3; 1; 6) |
(3; 3; 5) |
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7 |
(3; 5; 1) |
(0; 1; 5) |
(1; 0; 5) |
(7; 9;-1) |
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8 |
(5;-2; 4) |
(7; 1; 6) |
(7; 4; 5) |
(8; 4; 10) |
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9 |
(1; 2; 1) |
(9;-2; 2) |
(-3; 5; 0) |
(7; 8;-2) |
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10 |
(4; 1; 3) |
(2; 3; 6) |
(5;-3; 6) |
(3; 3; 5) |
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11 |
(3;-1; 2) |
(7; 2; 6) |
(9; 0; 6) |
(5; 1; 3) |
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12 |
(3; 5; 4) |
(1; 8; 6) |
(-1; 2; 6) |
(9;-1; 1) |
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13 |
(1; 1; 2) |
(-3; 9; 3) |
(-2; 5; 3) |
(7; 7;-1) |
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14 |
(1; 4; 3) |
(-1; 6; 6) |
(6;-4; 0) |
(2; 2; 1) |
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15 |
(2; 4; 1) |
(6; 7; 5) |
(7; 6; 5) |
(6; 8; 3) |
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16 |
(1; 2; 2) |
(3; 5; 4) |
(5;-1; 4) |
(7; 8; 5) |
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17 |
(2;-2; 1) |
(10; 2; 2) |
(6; 1; 2) |
(8; 4; 4) |
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18 |
(3; 4;-1) |
(1; 6; 2) |
(5; 5; 5) |
(1; 5; 1) |
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19 |
(2; 5; 3) |
(-1; 1; 7) |
(1;-1; 7) |
(4; 7; 2) |
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20 |
(1; 4; 2) |
(4; 2; 4) |
(7; 2; 3) |
(7; 1; 8) |
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21 |
(3; 1; 4) |
(7;-7; 5) |
(6;-3; 5) |
(9; 7; 7) |
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22 |
(2; 4; 3) |
(4; 6; 6) |
(-2; 3; 6) |
(4; 5; 5) |
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23 |
(5;-2;-1) |
(2;-6; 3) |
(3;-7; 3) |
(9; 2;-3) |
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24 |
(5; 2; 1) |
(7; 5; 3) |
(7; 8; 2) |
(8; 8; 7) |
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25 |
(2;-1; 7) |
(10;-5; 8) |
(-2; 2; 6) |
(8; 5; 4) |
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26 |
(4; 7; 8) |
(2; 9; 11) |
(5; 3; 11) |
(3; 9; 10) |
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27 |
(2; 1; 3) |
(6; 4; 7) |
(8; 2; 7) |
(4; 3; 4) |
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28 |
(1; 5; 2) |
(-1; 8; 4) |
(-3; 2; 4) |
(7;-1;-1) |
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29 |
(6; 1; 4) |
(2; 9; 5) |
(3; 5; 5) |
(12; 7; 1) |
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30 |
(6; 5; 1) |
(4; 7; 4) |
(11;-3;-2) |
(7; 3;-1) |
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31 |
(3; 1; 5) |
(7; 4; 9) |
(8; 3; 9) |
(7; 5; 7) |
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32 |
(3; 2; 6) |
(5; 5; 8) |
(7;-1; 8) |
(9; 8; 9) |
