Векторная алгебра. Машанов В.И - 20 стр.

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Задача 8
Найти 1)
{
}
;: abb
r
r
r
2) ,ab
r
r
если дан .b
r
N
a
r
b
r
N
a
r
b
r
1
)2,2,1(
a
r
9 16
)2,14,5(
a
r
30
2
)6,3,2(
a
r
14 17
)2,1,2(
a
r
12
3
)8,4,1(
a
r
9 18
)2,3,6(
a
r
21
4
)7,4,4(
a
r
18 19
)8,1,4(
a
r
18
5
)9,6,2(
a
r
20 20
)4,4,7(a
r
27
6
)7,6,6(a
r
33 21
)2,9,6(
a
r
33
7
)12,4,3(
a
r
26 22
)6,7,6(a
r
22
8
)14,5,2(a
r
30 23
)3,12,4(
a
r
13
9
)2,2,1(a
r
6 24
)2,5,14(
a
r
30
10
)6,3,2(a
r
21 25
)1,2,2(a
r
9
11
)8,4,1(a
r
18 26
)3,6,2(
a
r
21
12
)4,4,7(a
r
18 27
)8,1,4(a
r
18
13
)2,6,9(
a
r
22 28
)4,4,7(a
r
27
14
)6,7,6(a
r
33 29
)2,9,6(a
r
22
15
)3,12,4(
a
r
26 30
)6,9,2(
a
r
33
Задача 9
Найти ,,bac
r
r
r
если:
N
a
r
b
r
c
r
N
a
r
b
r
c
r
1
)2,2,1(a
r
)7,14,6(b
r
30 16
)1,4,8(a
r
)1,4,6( b
r
9
2
)8,4,1(a
r
)1,0,1(b
r
18 17
)1,2,2(
a
r
)3,2,16(b
r
15
3
)1,2,2(
a
r
)9,28,14( b
r
60 18
)1,4,8(
a
r
)2,4,5( b
r
18
4
)1,8,4(
a
r
)1,6,4(b
r
9 19
)1,2,2(
a
r
)3,10,4( b
r
45
5
)2,1,2(
a
r
)2,3,16( b
r
30 20
)1,4,8(
a
r
)3,4,4(b
r
18
6
)4,1,8(
a
r
)4,2,5( b
r
18 21
)2,1,2(
a
r
)8,1,6(b
r
15
7
)2,2,1(
a
r
)4,10,3( b
r
15 22
)8,1,4(
a
r
)1,1,0( b
r
27
8
)8,4,1(
a
r
)4,4,3(b
r
27 23
)2,1,2(a
r
)7,6,14(b
r
30
9
)2,1,2(a
r
)8,1,6( b
r
15 24
)8,1,4(a
r
)6,1,4( b
r
36
10
)8,1,4(a
r
)1,1,0(b
r
18 25
)2,1,2(
a
r
)28,9,14( b
r
15
11
)2,1,2(
a
r
)7,6,14( b
r
30 26
)8,1,4(
a
r
)5,2,4(b
r
9
12
)8,1,4(
a
r
)6,1,4(b
r
9 27
)1,2,2(
a
r
)3,16,2( b
r
45
13
)1,2,2(
a
r
)6,14,7( b
r
30 28
)1,8,4(
a
r
)3,4,4(b
r
18
14
)1,4,8(
a
r
)1,0,1(b
r
36 29
)1,2,2(
a
r
)3,4,10( b
r
15
15
)1,2,2(a
r
)9,14,28(b
r
15 30
)1,8,4(
a
r
)1,1,0(b
r
18
Задача 8
          {
          r r r
                 }
Найти 1) b : b a ;
           r r          r
      2) b a , если дан b .
    r                       r                  r                  r
N a                         b             N    a                  b
    r                                          r
 1 a (1,−2,2)             9               16   a (5,14,−2)        30
    r                                          r
 2 a (2,3,−6)             14              17   a (2,1,−2)         12
    r                                          r
 3 a (1,−4,8)             9               18   a (6,−3,2)         21
    r                                          r
 4 a (4,−4,7)             18              19   a (4,−1,8)         18
    r                                          r
 5 a (2,6,−9)             20              20   a (7,4,4)          27
    r                                          r
 6 a (6,6,7)              33              21   a (6,9,−2)         33
    r                                          r
 7 a (3,−4,−12)           26              22   a (6,7,6)          22
    r                                          r
 8 a (2,5,14)             30              23   a (4,−12,3)        13
    r                                          r
 9 a (1,2,2)              6               24   a (14,5,−2)        30
    r                                          r
10 a (2,3,6)              21              25   a (2,2,1)          9
    r                                          r
11 a (1,4,8)              18              26   a (2,6,−3)         21
    r                                          r
12 a (7,4,4)              18              27   a (4,1,8)          18
    r                                          r
13 a (9,−6,2)             22              28   a (7,4,4)          27
    r                                          r
14 a (6,7,6)              33              29   a (6,9,2)          22
    r                                          r
15 a (4,12,−3)            26              30   a (2,−9,6)         33


Задача 9
       r r r
Найти c ⊥ a , b , если:
    r                 r              r         r             r              r
N a                   b              c    N    a             b              c
    r                 r                        r             r
 1 a (1,2,2)          b (6,14,7)     30   16   a (8,4,1)     b (−6,−4,1)    9
    r                 r                        r             r
 2 a (1,4,8)          b (1,0,1)      18   17   a (−2,2,1)    b (−16,2,3)    15
    r                 r                        r             r
 3 a (2,−2,1)         b (14,−28,9)   60   18   a (−8,4,1)    b (5,−4,2)     18
    r                 r                        r             r
 4 a (4,−8,1)         b (−4,6,1)     9    19   a (−2,−2,1)   b (4,−10,3)    45
    r                 r                        r             r
 5 a (2,1,−2)         b (16,3,−2)    30   20   a (−8,−4,1)   b (4,4,3)      18
    r                 r                        r             r
 6 a (8,−1,−4)        b (−5,−2,4)    18   21   a (−2,1,−2)   b (−6,1,8)     15
    r                 r                        r             r
 7 a (1,−2,−2)        b (3,−10,4)    15   22   a (−4,1,−8)   b (0,1,−1)     27
    r                 r                        r             r
 8 a (1,−4,−8)        b (3,4,4)      27   23   a (2,1,2)     b (14,6,7)     30
    r                 r                        r             r
 9 a (2,1,2)          b (6,1,−8)     15   24   a (4,1,8)     b (−4,1,−6)    36
    r                 r                        r             r
10 a (4,1,8)          b (0,1,1)      18   25   a (2,1,−2)    b (14,9,−28)   15
    r                 r                        r             r
11 a (2,−1,2)         b (14,−6,7)    30   26   a (4,1,−8)    b (−4,2,5)     9
    r                 r                        r             r
12 a (4,−1,8)         b (4,1,6)      9    27   a (2,−2,1)    b (2,−16,3)    45
    r                 r                        r             r
13 a (2,−2,1)         b (7,−14,6)    30   28   a (4,−8,1)    b (−4,4,3)     18
    r                 r                        r             r
14 a (8,−4,1)         b (1,0,1)      36   29   a (−2,2,1)    b (−10,−4,3)   15
    r                 r                        r             r
15 a (2,2,1)          b (28,14,9)    15   30   a (−4,8,1)    b (0,1,1)      18