Разложение вектора по базису
Date: 2015-10-07; view: 415.
Действия над векторами
Даны точки А( 
), B( 
), C( 
). Вычислить: 
· 
; ( + )2; (3 -2 )·( +3 ).
Таблица 3.3 – Исходные данные
| № вар. | A
( )
| B
( )
| C
( )
|
| (2; -2; 4) | (3; 2; 6) | (4; -3; 5) | |
| (3; 1; -3) | (8; -4; -6) | (4; 2; 0) | |
| (7; 5; -2) | (6; 3; -2) | (4; 11; 2) |
Продолжение таблицы 3.3
| (1; 3; 10) | (-3; -5; -9) | (-15; 3; 6) | |
| (3; -6; -8) | (9; -5; -1) | (-3; -3; 7) | |
| (5; 3; 7) | (1; 5; -2) | (7; -11; 12) | |
| (10;6; 4) | (0; 3; 7) | (2; 14; 3) | |
| (5; 7; -3) | (6; 3; -4) | (5; 7; 11) | |
| (3; -8; -9) | (0; 5; 6) | (1; -6; -5) | |
| (3; 3; 8) | (-12; -4; 1) | (4; -6; 8) | |
| (0; -4; 11) | (2; 6; 10) | (1; 4; -4) | |
| (3; -4; 5) | (4; 15; 7) | (0; -16; -4) | |
| (1; 11; 10) | (2; 5; 11) | (4; -2; 5) | |
| (5; -5; -5) | (3; -4; 10) | (-6; 4; -8) | |
| (1;-9; 5) | (3; -3; 8) | (3; 13; 9) | |
| (1; -7; 4) | (-3; 4; 7) | (6; -4; 6) | |
| (7; -2; 7) | (5; 4; 5) | (-11; -6; -4) | |
| (4; -6; -6) | (2; -3; -5) | (0; 10; -6) | |
| (2; 4; -5) | (8; -1; -6) | (3; 4; 2) | |
| (0; 8; 6) | (1; 7; -7) | (6; 5; 12) | |
| (-4; 1; 8) | (-6; 7; 6) | (-9; 4; 10) | |
| (2; 7; -10) | (1; -1; 15) | (0; 20; -7) | |
| (1; 5; 7) | (-1; 12; 3) | (7; -5; 3) | |
| (0; -3; 8) | (-6; -10; -8) | (4; -3; 6) | |
| (-3; 4; 7) | (2; 4; 7) | (8; -1; 12) | |
| (-2; 5; -2) | (3; 10; -7) | (5; 6; -9) | |
| (5; 14; -2) | (0; 10; 4) | (0; 7; 7) | |
| (-3; -6; 3) | (-2; 4; 1) | (5; 12; -1) | |
| 29. | (-2; 2;-10) | (-8; 8; 10) | (3; -2; 18) |
| (5; 2; -2) | (4; 3; 3) | (8; 4; -7) |
3.4.1. Даны векторы 
( 
), 
( 
) и 
( 
). Найти разложение вектора ( 
) по базису , .
Таблица 3.4.1 – Исходные данные
| № вар. | ( )
| ( )
| ( )
| № вар. | ( )
| ( )
| ( )
|
| (2; 4) | (2; 6) | (4; -3) | (-7; 4) | (-3; 7) | (6; -4) | ||
| (3; -3) | (-4; -6) | (4; 2) | (-2; 7) | (5; 5) | (-11; -6) | ||
| (7; -2) | (3; -2) | (4; 11) | (-6; -6) | (2; -5) | (0; 10) | ||
| (1; 10) | (-5; -9) | (-15; 3) | (4; -5) | (8; -6) | (3; 4) | ||
| (3; -8) | (-5; -1) | (-3; -3) | (8; 6) | (1; -7) | (6; 5) | ||
| (5; 7) | (5; -2) | (7; -11) | (1; 8) | (-6; 6) | (-9; 4) | ||
| (10; 4) | (3; 7) | (2; 14) | (7; -10) | (1; 15) | (0; 20) | ||
| (5; -3) | (3; -4) | (5; 7) | (5; 7) | (-1; 3) | (7; -5) | ||
| (3; -9) | (5; 6) | (1; -6) | (-3; 8) | (-6; -8) | (4; -3) | ||
| (3; 8) | (-4; 1) | (4; -6) | (4; 7) | (2; 7) | (8; -1) | ||
| (0; 11) | (6; 10) | (1; 4) | (5; -2) | (3; -7) | (5; 6) | ||
| (3; 5) | (15; 7) | (0; -16) | (14; -2) | (0; 4) | (0; 7) | ||
| (1; 10) | (5; 11) | (4; -2) | (-6; 3) | (-2; 1) | (5; 12) | ||
| (5; -5) | (-4; 10) | (-6; 4) | (2;-10) | (-8; 10) | (3; -2) | ||
| (1; 5) | (-3; 8) | (3; 13) | (2; -2) | (4; 3) | (8; 4) |
3.4.2. Даны векторы ( 
), ( 
), ( 
) и 
( 
).
Найти разложение вектора ( 
) по базису , , .
Таблица 3.4.2 – Исходные данные
| № вар. | ( )
| ( )
| ( )
| ( )
|
| (2; 1; 3) | (-1; 2; 1) | (3; 2; -4) | (9; 3; -6) | |
| (2; 1; 4) | (-3; 5; 1) | (1; -4; -1) | (2; 5; -4) | |
| (2; 1; 3) | (-4; -2; -1) | (1; 4; 5) | (1; 3; 2) | |
| (2; 3; 1) | (-1; 2; -1) | (1; 2; 1) | (2; -2; -1) | |
| (1; 2; 1) | (1; -1; 3) | (3; 2; 4) | (5; 1; 6) | |
| (2; 3; 5) | (-1; -1; -3) | (1; 2; 4) | (2; 2; 4) | |
| (1; 1; 2) | (4; -1; 3) | (5; -2; 2) | (2; 1; -3) | |
| (2; 5; 1) | (2; -1; 3) | (-3; 8; 1) | (9; 4; 1) |
Продолжение таблицы 3.4.2
| (2; 5; 4) | (-3; 1; 3) | (1; -3; 2) | (17; -2; 16) | |
| (2; 1; 6) | (-4; 0; 1) | (-5; -3; 1) | (21; -18; 30) | |
| (1; 2; 1) | (3; -3; 2) | (-3; 3; 1) | (13; -10; 6) | |
| (2; 3; 4) | (-1; 1; -1) | (1; -1; 3) | (-4; -1; -7) | |
| (3; 2; 2) | (1; 3; 1) | (1; 1; 3) | (5; 1; 11) | |
| (1; 2; 4) | (1; -1; 1) | (2; 2; 4) | (-1; -4; -2) | |
| (2; 3; 3) | (-1; 4; -2) | (-1; -2; 4) | (4; 11; 11) | |
| (4; 1; 1) | (-1; 5; -3) | (-4; 2; 1) | (-3; 0; 6) | |
| (1; 2; 1) | (1; -3; 2) | (-2; 1; -1) | (-9; 2; 7) | |
| (3; 1; 2) | (4; -2; 1) | (-1; 2; 5) | (-4; 1; 3) | |
| (1; 2; 1) | (2; 3; -3) | (-1; 2; 1) | (3; 1; 2) | |
| (2; 1; 1) | (-1; -3; 1) | (1; 1; 4) | (9; 6; 8) | |
| (5; 1; 2) | (-3; 1; 3) | (4; -3; 1) | (4; 3; -2) | |
| (1; 1; 2) | (5; -10; 1) | (2; -3; -1) | (1; 9; -2) | |
| (5; 1; 2) | (-1; 1; -3) | (8; 6; -1) | (7; -3; 7) | |
| (1; 5; 1) | (-2; 1; 3) | (1; -3; 2) | (12; -2; 7) | |
| (3; 2; 1) | (-2; 4; -3) | (1; -3; -1) | (6; 5; 9) | |
| (2; 5; 4) | (-7; 1; 23) | (2; -1; -1) | (-14; 8; 58) | |
| (1; 2; 1) | (1; -1; 3) | (3; 1; -2) | (6; 3; 4) | |
| (3; 2; 2) | (2; 3; 1) | (1; -1; -3) | (6; 7; 1) | |
| (1; 2; 3) | (1; 3; 1) | (-5; 1; -1) | (5; 2; -1) | |
| (1; 2; 1) | (2; -1; 3) | (3; -1; 2) | (10; 8; -1) |
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