, .
b , . ab,* b((, b))., ,
(6.1) . |a| cosg= ba, (. .14), a |b| cosg = ab, :
. . , , .
:
1. : ab=ba
5. b() , , . . a ^b, ab=0. : ab=0 ¹ 0¹b, ^ b
.
, ( ) i, j, k:
, .
: , , (-4;-4;4), (-3;2;2),C(2; 5;1), D(3;-2;2), .
: BD, . : = (6;9;-3) BD = (6;-4;0). :
BD = 36 - 36 - 0 = 0.
, AC^BD. ABCD .
, .
:
a, b , , , b , , (. . 16).
b , :
1. a b, . . ^ ^b;
2. , , b (. . 17), . .
3. a, b .
b [,b]. i, j k(. . 18):
i j = k, j k = i, k i = j.
, , ij=k.
1) k^i, k^j;
2) |k|=1, | i x j| = |i| |J| sin(90)=1;
3) i, j k (. . 16).
1. , .. b=(ba) (. . 19).
b b , ( ), ( , b, b a, b, bxa ). axb = -(bxa).
|
|
2. , . . l(b) = (l)b = (lb).
l>0. l(b) b. (l)b b ( , l ). , l(b) (l)b . , . :
l(ab)=lb. l<0.
3. b , , . . ||b<=>b =0.
, i *i =j *j =k *k =0.
4. :
(a+b) = +b.