.
. 
, .
× = ï ïï ïcosj
:
1) × = ï ï2;
2) × = 0, ^ = 0 = 0.
3) × = × ;
4) ×( + 
) = × + × ;
5) (m )× = ×(m ) = m( × );
,
× = xa xb + ya yb + za zb;
, :
;
. (5 + 3 )(2 - ), 
10 × - 5 × + 6 × - 3 × = 10 
,
.. 
.
. , 
.
.. = (1, 2, 3), = (6, 4, -2)
× = 6 + 8 6 = 8:
.
cosj = 
. (3 - 2 )×(5 - 6 ), 
15 × - 18 × - 10 × + 12 × = 15 
+ 12×36 = 240 336 + 432 = 672 336 = 336.
. , 
.
.. = (3, 4, 5), = (4, 5, -3)
× = 12 + 20 - 15 =17:
.
cosj = 
. m 
.
= (m, 1, 0); = (3, -3, -4)
.
. 
, 
()() = 
= 10 +
+ 27 + 51 + 135 + 72 + 252 = 547.
.
. 
, :
1) 
, j - ,
2)
3) , .
: 
.
 |
j
:
1) 
;
2) 
, ïï = 0 = 0;
3) (m )´ = ´(m ) = m( ´ );
4) ´( + ) = ´ + ´ ;
5) (xa, ya, za) (xb, yb, zb) 
,
´ = 
6) , .
. 
.
= (2, 5, 1); = (1, 2, -3)
.
, . :
 |
Enter. Enter .
|
|
|
: Maple (Ó Waterloo Maple Inc.) , MapleV Release 4.
. (2, 2, 2), (4, 0, 3),
(0, 1, 0).
(2).
. , 
, 
.
, .. , .
. , 
, 
(2).
.
. , , , .
(, , ).
, , .
:
1) , :
) ;
) ;
) .
2) 
3) 
4) 
5) , , ,
6) 
, 
,
. , (5; 7; 2), B(3; 1; -1), C(9; 4; -4), D(1; 5; 0) .
: 
:
,
, , A, B, C D .
. , BCD, A(0; 0; 1), B(2; 3; 5), C(6; 2; 3), D(3; 7; 2).
: 
BCD.
S = 
(2)
.. V = 
; 
()
.
. , x, y, z .
.
. , :
Ax + By + Cz + D = 0,
, , 
- .
:
= 0
= 0
= 0 z
D = 0
= = 0
= = 0 z
= = 0 yOz
= D = 0
= D = 0
= D = 0 Oz
= = D = 0
= = D = 0 xOz
= = D = 0 yOz
, .
