Нахождение вектора по заданным условиям
Date: 2015-10-07; view: 460.
Смешанное произведение
Даны четыре точки А( 
), В( 
), C( 
) и D( 
). Вычислить объем треугольной пирамиды, построенной на векторах 
, 
, 
и высоту, опущенную из точки D, на плоскость основания. Является ли тройка векторов 
, 
, 
правой?
Таблица 3.8 – Исходные данные
| № вар. | А( )
| В( )
| C( )
| D( )
|
| (-3; 4; -7) | (1; 5; -4) | (-5; -2; 0) | (-12; 7; -1) | |
| (-1; 2; -3) | (4; -1; 0) | (2; 1; -2) | (1; -6; -5) | |
| (-3; -1; 1) | (-9; 1; -2) | (3; -5; 4) | (-7; 0; -1) | |
| (1; -1; 1) | (-2; 0; 3) | (2; 1; -1) | (-2; 4; 2) | |
| (1; 2; 0) | (1; -1; 2) | (0; 1; -1) | (2; -1; 4) | |
| (1; 0; 2) | (1; 2; -1) | (2; -2; 1) | (-5; -9; 1) | |
| (1; 2; -3) | (1; 0; 1) | (-2; -1; 6) | (3; -2; -9) | |
| (3; 10; -1) | (-2; 3; -5) | (-6; 0; -3) | (-6; 7; -10) | |
| (-1; 2; 4) | (-1; -2; -4) | (3; 0; -1) | (-2; 3; 5) | |
| (0; -3; 1) | (-4; 1; 2) | (2; -1; 5) | (-3; 4; -5) | |
| (1; 3; 0) | (4; -1; 2) | (3; 0; 1) | (4; 3; 0) | |
| (-2; -1; -1) | (0; 3; 2) | (3; 1; -4) | (-21; 20; -16) | |
| (-3; -5; 6) | (2; 1; -4) | (0; -3; -1) | (3; 6; 68) | |
| (2; -4; -3) | (5; -6; 0) | (-1; 3; -3) | (2; -10; 8) | |
| (1; -1; 2) | (2; 1; 2) | (1; 1; 4) | (-3; 2; 7) | |
| (1; 3; 6) | (2; 2; 1) | (-1; 0; 1) | (5; -4; 5) | |
| (-4; 2; 6) | (2; -3; 0) | (-10; 5; 8) | (-12; 1; 8) | |
| (7; 2; 4) | (7; -1; -2) | (-5; -2; -1) | (10; 1; 8) | |
| (2; 1; 4) | (3; 5; -2) | (-7; -3; 2) | (-3; 1; 8) | |
| (-1; -5; 2) | (-6; 0; -3) | (3; 6; -3) | (10; -8; -7) | |
| (0; -1; -1) | (-2; 3; 5) | (1; -5; -9) | (-4; -13; 6) | |
| (5; 2; 0) | (2; 5; 0) | (1; 2; 4) | (-3; -6; -8) | |
| (2; -1; -2) | (1; 2; 1) | (5; 0; -6) | (12; -3; 7) | |
| (-2; 0; -4) | (-1; 7; 1) | (4; -8; -4) | (-6; 5; 5) | |
| (14; 4; 5) | (-5; -3; 2) | (-2; -6; -3) | (-1; -8; 7) |
Продолжение таблицы 3.8
| (1; 2; 0) | (3; 0; -3) | (5; 2; 6) | (-13; -8; 16) | |
| (2; -1; 2) | (1; 2; -1) | (3; 2; 1) | (-5; 3; 7) | |
| (1; 1; 2) | (-1; 1; 3) | (2; -2; 4) | (2; 3; 8) | |
| (2; 3; 1) | (4; 1; -2) | (6; 3; 7) | (-5; -4; 8) | |
| (1; 1; -1) | (2; 3; 1) | (3; 2; 1) | (-3; -7; 6) |
Найти вектор 
, зная, что он перпендикулярен векторам 
и 
и удовлетворяет условию 
, где 
= (1, 2, -7).
Таблица 3.9 – Исходные данные
| № вар. |
(  )
|
(  )
| 
( 
| № вар. |
( 
|
( 
|
( )
|
| (1; 3; 10) | (-3; -5; -9) | (-15; 3; 6) | (2; 4; -5) | (8; -1; -6) | (3; 4; 2) | ||
| (3; -6; -8) | (9; -5; -1) | (-3; -3; 7) | (0; 8; 6) | (1; 7; -7) | (6; 5; 12) | ||
| (5; 3; 7) | (1; 5; -2) | (7; -11; 12) | (-4; 1; 8) | (-6; 7; 6) | (-9; 4; 10) | ||
| (10;6; 4) | (0; 3; 7) | (2; 14; 3) | (2; 7; -10) | (1; -1; 15) | (0; 20; -7) | ||
| (5; 7; -3) | (6; 3; -4) | (5; 7; 11) | (1; 5; 7) | (-1; 12; 3) | (7; -5; 3) | ||
| (3; -8; -9) | (0; 5; 6) | (1; -6; -5) | (0; -3; 8) | (-6; -10;-8) | (4; -3; 6) | ||
| (3; 3; 8) | (-12; -4; 1) | (4; -6; 8) | (-3; 4; 7) | (2; 4; 7) | (8; -1; 12) | ||
| (0; -4; 11) | (2; 6; 10) | (1; 4; -4) | (-2; 5; -2) | (3; 10; -7) | (5; 6; -9) | ||
| (3; -4; 5) | (4; 15; 7) | (0; -16; -4) | (5; 14; -2) | (0; 10; 4) | (0; 7; 7) | ||
| (1; 11; 10) | (2; 5; 11) | (4; -2; 5) | (-3; -6; 3) | (-2; 4; 1) | (5; 12; -1) | ||
| (5; -5; -5) | (3; -4; 10) | (-6; 4; -8) | (-2; 2;-10) | (-8; 8; 10) | (3; -2; 18) | ||
| (1;-9; 5) | (3; -3; 8) | (3; 13; 9) | (5; 2; -2) | (4; 3; 3) | (8; 4; -7) | ||
| (2; -2; 4) | (3; 2; 6) | (4; -3; 5) | (1; -7; 4) | (-3; 4; 7) | (6; -4; 6) | ||
| (3; 1; -3) | (8; -4; -6) | (4; 2; 0) | (7; -2; 7) | (5; 4; 5) | (-11; -6; -4) | ||
| (7; 5; -2) | (6; 3; -2) | (4; 11; 2) | (4; -6; -6) | (2; -3; -5) | (0; 10; -6) |
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