Завдання 16
Задано
координати
вершин піраміди
Скласти чи знайти:
об’єм піраміди;
а) рівняння і б) площу основи
а) рівняння і б) довжину висоти
проведеної
з вершини
косинус внутрішнього кута між гранями
і
координати
точки перетину висоти
з площиною
Номер варіанта |
А |
В |
С |
D |
1 |
(1; –1; 3) |
(5; –6; 4) |
(3; 4; –3) |
(6; 1; –6) |
2 |
(2; 3; 1) |
(4; 5; –2) |
(6; 2; 4) |
(–2; 1; 3) |
3 |
(–4; 1; 3) |
(1; –4; 1) |
(–3; 5; 6) |
(–1; 7; 2) |
4 |
(3; 4; 5) |
(7; 0; 1) |
(6; 4; 2) |
(8; 3; 7) |
5 |
(2; 5; 6) |
(4; 7; 9) |
(–3; 8; 1) |
(0; 6; 4) |
6 |
(4; 0; 3) |
(0; 2; 2) |
(1; 5; 4) |
(3; 10; 5) |
7 |
(3; 1; 5) |
(6; 4; 4) |
(0; 3; 4) |
(4; 2; 5) |
8 |
(3; 2; 2) |
(4; 1; 0) |
(0; 3; 4) |
(3; 4; 7) |
9 |
(2; 2; 0) |
(3; 0; 4) |
(4; 6; 1) |
(5; 7; 2) |
10 |
(2; 0; 1) |
(5; 5; 3) |
(4; 2; –1) |
(5; –2; 4) |
11 |
(–1; 5; 3) |
(–3; 7; 6) |
(2; 3; 4) |
(4; 6; 1) |
12 |
(3; 5; 4) |
(5; 7; 2) |
(2; 8; 1) |
(6; 4; 3) |
13 |
(–2; 1; –6) |
(–3; 2; –4) |
(–4; 2; –7) |
(5; 6; 8) |
14 |
(2; 1; –1) |
(4; 3; –4) |
(3; 5; 2) |
(5; 7; 7) |
15 |
(2; 4; 7) |
(4; 6; 8) |
(6; 9; 1) |
(–2; 4; 3) |
16 |
(3; 2; 4) |
(7; 2; 1) |
(4; –2; 1) |
(–4; 5; 6) |
17 |
(–1; 1; 5) |
(–1; 5; 2) |
(3; 2; 6) |
(0; 4; –1) |
18 |
(4; 6; 2) |
(3; 1; 1) |
(–1; 5; 4) |
(7; 8; 3) |
19 |
(2; 3; 1) |
(3; 4; 2) |
(8; 3; 5) |
(–4; 7; 6) |
20 |
(4; 6; 4) |
(8; 9; 5) |
(6; 8; –1) |
(2; 4; 6) |
21 |
(3; 2; 1) |
(4; 5; 2) |
(6; 2; 4) |
(–4; 6; 5) |
Номер варіанта |
А |
В |
С |
D |
22 |
(1; 0; –2) |
(2; –2; 1) |
(4; 4; –1) |
(5; 6; 2) |
23 |
(2; 5; 4) |
(5; 7; 0) |
(–1; 8; 1) |
(–2; 4; 3) |
24 |
(2; 1; 0) |
(4; –2; 3) |
(6; 4; –3) |
(2; 8; 4) |
25 |
(1; 0; –2) |
(2; –2; 3) |
(4; 3; –1) |
(6; 2; 5) |
26 |
(4; 8; 3) |
(7; 6; 4) |
(1; 9; 5) |
(1; 2; 6) |
27 |
(–1; 1; 1) |
(3; 0; 4) |
(0; 4; 5) |
(2; 7; 1) |
28 |
(3; 1; 2) |
(5; –1; –1) |
(4; 3; 6) |
(–2; 5; 4) |
29 |
(–2; –1; –3) |
(–5; 1; –6) |
(–4; 3; –2) |
(1; 0; 3) |
30 |
(0; 4; –2) |
(2; 6; –1) |
(–2; –1; –3) |
(4; 7; 1) |