. .
. ={X1,X2,...Xn} n- . (X1,X2,X3). n=1,2,3. - . | AB |=| a | - . 2 . , 1 ||- . . , 1- ||- . 2 , , , - .
1. : l . , . -: ) || . ) l>0, , l<0, ¯ . )l>1, < ,)l<1, > . 2. n , n: /n= a *(1/n).
3. - . 1- . 4. - c, , .
. .
2 , .
. 3 .
. .
= OA + OB, OA =x* i, OB =j*y, OC =x i +y j. , -
.
=1 i +y1 j +z1 k; b =2 i +y2 j +z2 k
l* a =l(1 i +y1 j +z1 k)= l(1) i +l (y1) j +l(z1) k
a b =(x1x2) i +(y1y2) j +(z1z2) k
ab =x1x2 ii +y1x2 ij +x2z1 ki +x1y2 ij +y1y2 jj + z1y2 kj +x1z1 ik +y1z2 jk +z1z2 kk =x1x2+y1y2+z1z2
ii =1; ij =0; ..
2 .
=x2+y2+z2=| a |2 a {x,y,z}, aa =| a |*| a |, a 2=| a| 2
ab =|a|*|b|*cosj
) =0,<=> ^ , x1x2+y1y2+z1z2=0
) || - , , x1/x2=y1/y2=z1/z2
.
-(skala-) 2 . , cos . (, )- . * =| |*| |*cosj, j=p/2, cosp/2=0, a^b=> ab =0. 0 ().
2 .
-----
, , . (), 3 1 2 . . 1 2 . - . 2 . , : 1. | c |=| a |*| b |*sinj. 2. c ^ a c ^ b. 3. , , -.
|
|
.
. - , : a * b * c =[ a * b ]* c = a *[ b * c ],
a ={ax,ay,az}
b ={bx,by,bz}
c ={cx,cy,cz}
-:
1. 2 :
a * b * c =- b * c * a
2. :
a * b * c = c * a * b = b * c * a
3.)(. ) 3 . a * b * c =0
) a, b, c 1 , | a * b * c |=V,
a * b * c >0, a, b, c -
a * b * c <0, a, b, c -