– Вычислить объём тетраэдра с вершинами в точках А1, A2, А3, А4;
– угол между рёбрами А1, A2 и А3, А4;
– величину двухгранного угла А1 А2 А3 и А4 А2 А3;
– уравнение высоты, опущенной из вершины А4 на грань А1 А2 А3;
– проекцию вершины А4 на грань А1 А2 А3;
– расстояние от точки А4 до плоскости А1, A2, А3;
– площадь грани А1, A2, А3.
| А1 | А2 | А3 | А4 | |
| 1 | (1, 3, 6) | (2, 2, 1) | (– 1, 0, 1) | (– 4, 6, – 3) |
| 2 | (– 4, 2, 6) | (2, – 3, 0) | (– 10, 5, 8) | (– 5, 2, – 4) |
| 3 | (7, 2, 4) | (7, – 1, – 2) | (3, 3, 1) | (– 4, 2, 1) |
| 4 | (2, 1, 4) | (– 1, 5, - 2) | (– 7, - 3, 2) | (– 6, – 3, 6) |
| 5 | (– 1, – 5, 2) | (– 6, 0, – 3) | (3, 6, – 3) | (– 10, 6, 7) |
| 6 | (0, – 1, – 1) | (– 2, 3, 5) | (1, – 5, – 9) | (– 1, – 6, 3) |
| 7 | (5, 2, 0) | (2, 5, 0) | (1, 2, 4) | (– 1, 1, 1) |
| 8 | (2, – 1, – 2) | (1, 2, 1) | (5, 0, – 6) | (– 10, 9, – 7) |
| 9 | (– 2, 0, – 4) | (– 1, 7, 1) | (4, – 8, – 4) | (1, – 4, 6) |
| 10 | (14, 4, 5) | (– 5, – 3, 2) | (– 2, – 6, – 3) | (– 2, 2, – 1) |
| 11 | (1, 2, 0) | (3, 0, – 3) | (5, 2, 6) | (8, 4, – 9) |
| 12 | (2, – 1, 2) | (1, 2, – 1) | (3, 2, 1) | (– 4, 2, 5) |
| 13 | (1, 1, 2) | (– 1, 1, 3) | (2, – 2, 4) | (– 1, 0, – 2) |
| 14 | (2, 3, 1) | (4, 1, – 2) | (6, 3, 7) | (7, 5, – 3) |
| 15 | (1, 1, – 1) | (2, 3, 1) | (3, 2, 1) | (5, 9, – 8) |
| 16 | (1, 5, – 7) | (– 3, 6, 3) | (– 2, 7, 3) | (– 4, 8, – 12) |
| 17 | (– 3, 4, – 7) | (1, 5, – 4) | (– 5, – 2, 0) | (2, 5, 4) |
| 18 | (– 1, 2, – 3) | (4, – 1, 0) | (2, 1, – 2) | (3, 4, 5) |
| 19 | (4, – 1, 3) | (– 2, 1, 0) | (0, – 5, 1) | (3, 2, – 6) |
| 20 | (1, – 1, 1) | (– 2, 0, 3) | (2, 1, – 1) | (2, – 2, – 4) |
| 21 | (1, 2, 0) | (1, – 1, 2) | (0, 1, – 1) | (– 3, 0, 1) |
| 22 | (1, 0, 2) | (1, 2, – 1) | (2, – 2, 1) | (2, 1, 0) |
| 23 | (1, 2, – 3) | (1, 0, 1) | (– 2, – 1, 6) | (0, – 5, – 4) |
| 24 | (– 1, 2, 4) | (– 1, – 2, – 4) | (3, 0, – 1) | (7, – 3, 1) |
| 25 | (0, – 3, 1) | (– 4, 1, 2) | (2, – 1, 5) | (3, 1, – 4) |
| 26 | (1, 3, 0) | (4, – 1, 2) | (3, 0, 1) | (– 4, 3, 5) |
| 27 | (– 2, – 1, – 1) | (0, 3, 2) | (3, 1, – 4) | (– 4, 7, 3) |
| 28 | (– 3, – 5, 6) | (2, 1, – 4) | (0, – 3, – 1) | (– 5, 2, – 8) |
| 29 | (2, – 4, – 3) | (5, – 6, 0) | (– 1, 3, – 3) | (– 10, – 8, 7) |
| 30 | (1, – 1, 2) | (2, 1, 2) | (1, 1, 4) | (6, – 3, 8) |