Аналитическая геометрия. Часть II. Аналитическая геометрия пространства. Шурыгин В.В. - 23 стр.

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c = a d = b
P (a, b) a b
S
P (a,b)
=
p
det G(a, b).
[[a, b], [c, d]] = b(a, c, d) − a(b, c, d).
u = [c, d]
[[a, b], u] [[a, b], [c, d]] = [[a, b], u] =
b(a, u) − a(b, u) = b(a, [c, d]) − a(b, [c, d]) = b(a, c, d) − a(b, c, d)
2
L(a, b) L(c, d)
c
b
a
d
w
[[a, b], [c, d]] = [[d, c], [a, b]] =
c(a, b, d) − d(a, b, c).
w = [[a, b], [c, d]]
L(a, b)
L(c, d)
(a, b, c)(u, v, w) =
(a, u) (a, v) (a, w)
(b, u) (b, v) (b, w)
(c, u) (c, v) (c, w)
.
E
3
{e
i
} (a, b, c) = detA (u, v, w) = detB
A =
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
, B =
u
1
u
2
u
3
v
1
v
2
v
3
w
1
w
2
w
3
.
detA detB = det(AB) (a, b, c)(u, v, w) =
?+1003 9 << c = a O d = b O ,+1(0)4 -1)CA A F+41 C13 9(-1)B
3 ,1+ 0C ,0011)1+0440 P (a, b) O ,+-2+)++ 0 9).2+0E a  b ~
                                            p
                               SP (a,b) =       det G(a, b).
   °' NfjqhIMhf rIhLokfifMLf ikHg kfjqhIMJg rIhLokfifML¡'
                                                                                   
                      [[a, b], [c, d]] = b(a, c, d) − a(b, c, d).              <ˆ
   ½hjnonqfŸ¾pqkh' *+:0(4 u = [c, d]  9+-,+17:)4-3 <= C13 C9+DB
++ 9).2+++ ,+:9)C)3 [[a, b], u]  4))4~ [[a, b], [c, d]] = [[a, b], u] =
                                                                         
b(a, u) − a(b, u) = b(a, [c, d]) − a(b, [c, d]) = b(a, c, d) − a(b, c, d) 2
   #mãL¡ kfjqhI ikHg rŸhpjhpqf¡ L(a, b) L L(c, d) '
   ?+17:3-7 .+-+-44)2(+-27A 9).2+++ ,+:9)C)3  F+41+D
   
<ˆ O ,+1(0)4
                                                                      w
      [[a, b], [c, d]] = [[d, c], [a, b]] =
                                                          a                    d
           c(a, b, d) − d(a, b, c).
2-AC0 -1)C)2O (2+ 9).2+
             w = [[a, b], [c, d]]                                              b
                                                         c
,0C1)s2 .0sC+D : ,1+-.+-2)D L(a, b)
 L(c, d) O -4 -+. €=                                         -  €=
   Ì' eIhLokfifMLf ikHg plfžnMMJg rIhLokfifML¡'
                                       (a, u) (a, v) (a, w)
                                                                                       
                  (a, b, c)(u, v, w) = (b, u) (b, v) (b, w) .                      <Š
                                       (c, u) (c, v) (c, w)
   ½hjnonqfŸ¾pqkh' *))4 9 E ).+2+D ,09D +2++4+90D
*0:- {ei}  +C0 (a, b, c) = detA O 0 (u, v, w) = detB O C)
                                  3


                                                            
                       a1 a2 a3                       u1 u2 u3
                                                            
                 A =  b1 b2 b3  ,             B =  v1 v2 v3  .
                       c1 c2 c3                       w1 w2 w3
Ñ+410 <Š 2),)7 -1)C)2 : :9)-2++ -4 ª—« O 1 ˆO ®€ˆ 402(+B
+ 2+sC)-290 detA detB = det(AB)  )D-292)17+O (a, b, c)(u, v, w) =
                                 ڌ

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