Задание № 2
По четырем заданным точкам построить пирамиду и средствами векторной алгебры найти: 1) длину ребра А1А2; 2) угол между ребрами А1А2 и А1А4; 3) площадь грани А1А2А3; 4) объем пирамиды А1А2А3А4; 5) составить уравнение прямой А1А2; 6) уравнение плоскости А1А2А3.
Координаты вершин пирамиды даны в таблице 3.
Таблица 3
№ варианта |
А1 |
А2 |
А3 |
А4 |
2.1. |
(1, 1, 1) |
(–1, 2, 4) |
(2, 0, 6) |
(–2, 5, –1) |
2.2. |
(0, 5, 0) |
(2, 3, –4) |
(0, 0, –6) |
(–3, 1, –1) |
2.3. |
(0, 0, 6) |
(4, 0, –4) |
(1, 3, –1) |
(4, –1, –3) |
2.4. |
(2, –5, 3) |
(3, 2, –5) |
(5, 3, 2) |
(–5, 3, 2) |
2.5. |
(6, 0, 4) |
(0, 6, 4) |
(4, 6, 0) |
(0, –6, 4) |
2.6. |
(3, 2, 4) |
(2, 4, 3) |
(4, 3, –2) |
(–2, –4,–3) |
2.7. |
(6, 3, 5) |
(5, –4, 3) |
(3, 5, 6) |
(–6, –1, 2) |
2.8. |
(5, –2, –1) |
(4, 0, 0) |
(2, 5, 1) |
(1, 2, 5) |
2.9. |
(4, 2, 5) |
(3, 0, 4) |
(0, 0, 3) |
(5, –2, –4) |
2.10. |
(4, 2, –5) |
(3, 0, 4) |
(0, 2, 3) |
(5, –2, –4) |
2.11. |
(4, 4, 10) |
(7, 10, 2) |
(2, 8, 4) |
(9, 6, 9) |
2.12. |
(4, 6, 5) |
(6, 9, 4) |
(2, 10, 10) |
(7, 5, 9) |
2.13. |
(3, 5, 4) |
(8, 7, 4) |
(5, 10, 4) |
(4, 7, 8) |
2.14. |
(10, 6, 6) |
(–2, 8, 4) |
(6, 8, 9) |
(7, 10, 3) |
2.15. |
(1, 8, 2) |
(5, 2, 6) |
(5, 7, 4) |
(4, 10, 9) |
2.16. |
(6, 6, 5) |
(4, 9, 5) |
(4, 6, 11) |
(6, 9, 3) |
2.17. |
(7, 2, 2) |
(5, 7, 7) |
(5, 3, 1) |
(2, 3, 7) |
2.18. |
(8, 6, 4) |
(10, 5, 5) |
(5, 6, 8) |
(8, 10, 7) |
2.19. |
(7, 7, 3) |
(6, 5, 8) |
(3, 5, 8) |
(8, 4, 1) |
2.20. |
(–2, 1, 2) |
(4, 0, 0) |
(3, 2, 7) |
(1, 3, 2) |
2.21. |
(3, 2, 7) |
(1, 3, 2) |
(–2, 1, 2) |
(4, 0, 0) |
2.22. |
(1, 3, 2) |
(3, 2, 7) |
(4, 0, 0) |
(–2, 1, 2) |
2.23. |
(3, 1, –2) |
(1, –2, 1) |
(2, 2, 5) |
(–2, 1, 0) |
2.24. |
(–2, 1, 0) |
(2, 2, 5) |
(3, 1, 2) |
(1, –2, 1) |
2.25. |
(2, 2, 5) |
(–2, 1, 0) |
(1, –2, 1) |
(3, 1, 2) |
2.26. |
(1, –1, 6) |
(4, 5, –2) |
(–1, 3, 0) |
(1, –1, 5) |
2.27. |
(6, 1, 5) |
(–1, 3, 0) |
(4, 5, –2) |
(1, –1, 6) |
2.28. |
(1, –2, 1) |
(3, 1, –2) |
(2, 2, 5) |
(–2, 1, 0) |
2.29. |
(4, 0, 0) |
(–2, 1, 2) |
(1, 3, 2) |
(3, 2, 7) |
2.30. |
(–5, 6, –1) |
(6, –5, 2) |
(6, 5, 1) |
(0, 0, 2) |