Векторная алгебра. Машанов В.И - 25 стр.

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Задача 14
Найти составляющие h
r
и g
r
вектора ,c
r
ортогональную и компланарную векторам a
r
и .b
r
N
a
r
b
r
c
r
1
)1,0,2(a
r
)1,1,0( b
r
)1,1,5(
c
r
2
)1,6,3(c
r
)0,16,8(b
r
)3,1,3(c
r
3
)1,1,5(
a
r
)1,3,9( b
r
)4,1,0(
c
r
4
)3,1,2(
a
r
)10,4,7( b
r
)0,0,3(c
r
5
)3,1,3(
a
r
)4,0,2(b
r
)0,4,1(c
r
6
)1,2,1(
a
r
)3,4,0( b
r
)3,3,4(c
r
7
)2,3,2(
a
r
)4,8,5( b
r
)1,1,5(c
r
8
)3,3,2(
a
r
)3,5,2( b
r
)1,1,5(
c
r
9
)1,1,1(a
r
)4,3,3(b
r
)1,3,3(
c
r
10
)1,2,1(
a
r
)1,4,1( b
r
)1,0,5(
c
r
11
)0,4,1(a
r
)1,10,3( b
r
)1,1,5(c
r
12
)0,5,1(
a
r
)1,8,2( b
r
)1,2,6(
c
r
13
)2,2,1(a
r
)3,1,0(b
r
)0,2,5(
c
r
14
)4,1,2(
a
r
)13,1,5( b
r
)4,3,4(c
r
15
)4,1,4(a
r
)7,1,10(b
r
)1,5,1(
c
r
16
)5,2,1(a
r
)16,4,4(b
r
)0,1,4(
c
r
17
)1,3,3(
a
r
)2,8,7( b
r
)2,0,4(c
r
18
)1,1,4(
a
r
)1,2,6( b
r
)2,1,3(
c
r
19
)1,1,1(
a
r
)4,1,2( b
r
)2,1,6(
c
r
20
)2,0,1(a
r
)5,2,3( b
r
)1,1,5(
c
r
21
)0,1,1(a
r
)3,1,0(b
r
)2,2,5(
c
r
22
)1,1,2(
a
r
)2,4,5( b
r
)4,0,1(c
r
23
)2,1,1(
a
r
)6,1,2( b
r
)1,0,5(c
r
24
)1,3,2(a
r
)2,2,4(b
r
)1,1,3(
c
r
25
)0,6,2(
a
r
)1,5,1( b
r
)1,0,4(
c
r
26
)1,1,1(
a
r
)1,3,0( b
r
)2,0,4(c
r
27
)3,2,2(a
r
)3,2,3(b
r
)5,1,1(
c
r
28
)1,1,1(
a
r
)4,3,1(b
r
)1,3,3(
c
r
29
)1,3,0(a
r
)3,11,1(b
r
)3,1,3(
c
r
30
)2,1,2(a
r
)4,2,3(b
r
)3,1,1(
c
r
Задача 14
                   r   r            r                                      r r
Найти составляющие h и g вектора c , ортогональную и компланарную векторам a и b .
    r                    r                       r
N a                      b                       c
    r                    r                       r
 1 a (2,0,1)             b (0,−1,−1)             c (5,1,−1)
    r                    r                       r
 2 c (3,6,1)             b (8,16,0)              c (3,1,3)
    r                    r                       r
 3 a (5,1,−1)            b (9,3,−1)              c (0,−1,4)
    r                    r                       r
 4 a (2,1,−3)            b (7,4,−10)             c (3,0,0)
    r                    r                       r
 5 a (3,−1,3)            b (2,0,4)               c (1,4,0)
    r                    r                       r
 6 a (1,−2,1)            b (0,−4,3)              c (4,3,3)
    r                    r                       r
 7 a (2,−3,2)            b (5,−8,4)              c (5,1,1)
    r                    r                       r
 8 a (2,3,−3)            b (2,5,−3)              c (5,1,−1)
    r                    r                       r
 9 a (1,1,1)             b (3,3,4)               c (3,−3,1)
    r                    r                       r
10 a (1,2,−1)            b (1,4,−1)              c (5,0,−1)
    r                    r                       r
11 a (1,4,0)             b (3,10,−1)             c (5,1,1)
    r                    r                       r
12 a (1,−5,0)            b (2,−8,1)              c (6,−2,−1)
    r                    r                       r
13 a (1,2,2)             b (0,1,3)               c (5,−2,0)
    r                    r                       r
14 a (2,−1,4)            b (5,−1,13)             c (4,3,4)
    r                    r                       r
15 a (4,1,4)             b (10,1,7)              c (−1,5,−1)
    r                    r                       r
16 a (1,2,5)             b (4,4,16)              c (4,−1,0)
    r                    r                       r
17 a (3,3,−1)            b (7,8,−2)              c (4,0,2)
    r                    r                       r
18 a (4,1,−1)            b (6,2,−1)              c (3,−1,2)
    r                    r                       r
19 a (1,1,−1)            b (2,1,−4)              c (6,1,−2)
    r                    r                       r
20 a (1,0,2)             b (3,−2,5)              c (5,−1,−1)
    r                    r                       r
21 a (1,1,0)             b (0,1,3)               c (5,−2,−2)
    r                    r                       r
22 a (2,1,−1)            b (5,4,−2)              c (1,0,4)
    r                    r                       r
23 a (1,1,−2)            b (2,1,−6)              c (5,0,1)
    r                    r                       r
24 a (2,3,1)             b (4,2,2)               c (3,−1,−1)
    r                    r                       r
25 a (2,−6,0)            b (1,−5,−1)             c (4,0,−1)
    r                    r                       r
26 a (−1,−1,1)           b (0,−3,1)              c (4,0,2)
    r                    r                       r
27 a (2,2,3)             b (3,2,3)               c (1,−1,5)
    r                    r                       r
28 a (− 1,1,1)           b (−1,3,4)              c (3,3,−1)
    r                    r                       r
29 a (0,3,1)             b (−1,11,3)             c (3,−1,−3)
    r                    r                       r
30 a (2,1,2)             b (3,2,4)               c (1,−1,3)