Векторная алгебра. Машанов В.И - 16 стр.

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28
bababa
r
r
r
r
r
r
52;43;3;4 +−−
°=== 60),(;1;2 baba
r
r
r
r
29
bababa
r
r
r
r
r
r
36;25;5;3 +−−
°=== 60),(;2;1 baba
r
r
r
r
30
bababa
r
r
r
r
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r
23;36;4;5 +−−
°=== 45),(;3;2 baba
r
r
r
r
Задача 2
В правильном шестиугольнике ABCDEF с центром О:
N Дано Найти
1
bCAaBA
r
r
r
r
== , FCEBDA
r
r
r
,,
2
bEAaCA
r
r
r
s
== , DCCBBA
r
r
r
,,
3
bECaCA
r
r
r
s
== , FCEBDA
r
r
r
,,
4
bEBaDA
r
r
r
r
== , AEECCA
r
r
r
,,
5
bCEaCA
r
r
r
s
== , FDDBFB
r
r
r
,,
6
bDFaEF
r
r
r
r
== , AEECCA
r
r
r
,,
7
bCEaAE
r
r
r
r
== , DCCBBA
r
r
r
,,
8
bCFaDA
r
r
r
r
== , FDDBBF
r
r
r
,,
9
bBAaDA
r
r
r
r
== , AEECCA
r
r
r
,,
10
bDAaEA
r
r
r
r
== , DFDBFB
r
r
r
,,
11
bBAaFA
r
r
r
r
== , FCEBDA
r
r
r
,,
12
bAEaCE
r
r
r
r
== , DCCBBA
r
r
r
,,
13
bEAaDA
r
r
r
r
== , BFFDDB
r
r
r
,,
14
bDBaFB
r
r
r
r
== , DCCBBA
r
r
r
,,
15
bFCaEB
r
r
r
r
== , AEECCA
r
r
r
,,
16
bECaCA
r
r
r
s
== , BFFDDB
r
r
r
,,
17
bFAaBA
r
r
r
r
== , AEECCA
r
r
r
,,
18
bDFaBF
r
r
r
r
== , FCEBDA
r
r
r
,,
19
bEOaCO
r
r
r
s
== , AEECCA
r
r
r
,,
20
bEAaCA
r
r
r
s
== , AOEOCO
r
r
r
,,
21
bDFaCF
r
r
r
r
== , DCCBBA
r
r
r
,,
22
bDOaFO
r
r
r
r
== , BDDFFB
r
r
r
,,
23
bCFaBF
r
r
r
r
== , EDDCCB
r
r
r
,,
24
bOAaCA
r
r
r
s
== , BDDFFB
r
r
r
,,
25
bCOaDO
r
r
r
r
== , AEECCA
r
r
r
,,
26
bDCaCB
r
r
r
s
== , BDDFFB
r
r
r
,,
27
bCAaDA
r
r
r
r
== , DCCBBA
r
r
r
,,
28
bCFaDA
r
r
r
r
== , FDDBBF
r
r
r
,,
29
bCFaDF
r
v
r
r
== , AEECCA
r
r
r
,,
30
bDEaCE
r
r
r
s
== , DOCOBO
r
r
r
,, 
      r r r         r r      r               r       r      r r
28   4a;−3b ;3a − 4b ;2a + 5b                a = 2; b = 1; (a , b ) = 60°
      r r r         r r      r               r      r       r r
29   3a ;−5b ;5a − 2b ;6a + 3b               a = 1; b = 2; (a , b ) = 60°
      r r r         r r      r               r       r      r r
30   5a ;−4b ;6a − 3b ;3a + 2b               a = 2; b = 3; (a , b ) = 45°



Задача 2
В правильном шестиугольнике ABCDEF с центром О:
N Дано                                  Найти
      r        r r                        r r r
 1 AB = ar , AC = b                      AD , BE , C F
      s        r r                        r r r
 2 AC = ar , AE = b                      AB , BC , C D
      s        r r                        r r r
 3 AC = ar , CE = b                      AD , BE , C F
      r        r r                        r r r
 4 AD = ar, BE = b                       AC , C E , EA
      s        r r                        r r r
 5 AC = ar , EC = b                     BF , BD, DF
      r       r r                         r r r
 6 FE = ar , FD = b                      AC , C E , EA
      r       r r                         r r r
 7 EA = ar , EC = b                      AB , BC , C D
      r        r r                        r r r
 8 AD = ar, FC = b                      FB, BD, DF
      r        r r                        r r r
 9 AD = ar, AB = b                       AC , C E , EA
      r        r r                        r r r
10 AE = ar, AD = b                      BF , BD , FD
      r        r r                        r r r
11 AF = ar, AB = b                       AD , BE , C F
      r       r r                         r r r
12 EC = ar , EA = b                      AB , BC , C D
      r        r r                        r r r
13 AD = ar, AE = b                      BD, DF , FB
      r        r r                        r r r
14 BF = ar , BD = b                      AB , BC , C D
      r       r r                         r r r
15 BE = ar , CF = b                      AC , C E , EA
      s        r r                        r r r
16 AC = ar , CE = b                     BD, DF , FB
      r        r r                        r r r
17 AB = ar , AF = b                      AC , C E , EA
      r       r r                         r r r
18 FB = ar , FD = b                      AD , BE , C F
      s        r r                        r r r
19 OC = ar , OE = b                      AC , C E , EA
      s        r r                        r r r
20 AC = ar , AE = b                     OC , OE , OA
      r        r r                        r r r
21 FC = ar , FD = b                      AB , BC , C D
      r        r r                        r r r
22 OF = ar , OD = b                     BF , FD, DB
      r       r r                         r r r
23 FB = ar , FC = b                     BC , CD, DE
      s        r r                        r r r
24 AC = ar , AO = b                     BF , FD, DB
      r        r r                        r r r
25 OD = ar, OC = b                       AC , C E , EA
      s        r r                        r r r
26 BC = ar , CD = b                     BF , FD, DB
      r        r r                        r r r
27 AD = ar, AC = b                       AB , BC , C D
      r        r r                        r r r
28 AD = ar, FC = b                      FB, BD, DF
      r        v r                        r r r
29 FD = ar , FC = b                      AC , C E , EA
      s        r r                        r r r
30 EC = ar , ED = b                     OB, OC , OD

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