1. a, b . :
) ;
) ;
) ;
) , ;
) , .
| . . | . | .. | ||||
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2. , , D. :
) ;
) ABCD.
| ( ) | |||||
| A(3, 4, 5) | (1, 2, 1) | (-2, -3, 6) | D(3, -6, -3) | ACD | |
| (-7, -5, 6) | (-2, 5, -3) | (3, -2, 4) | D(l, 2, 2) | BCD | |
| A(1, 3, 1) | (-1, 4, 6) | (-2, -3, 4) | D(3, 4, -4) | ACD | |
| (2, 4, 1) | (-3, -2, 4) | (3, 5, -2) | D(4, 2, -3) | ABD | |
| A(-5, -3, -4) | (1, 4, 6) | (3, 2, -2) | D(8, -2, 4) | ACD | |
| A(3, 4, 2) | (-2, 3, -5) | (4, -3, 6) | D(6, -5, 3) | ABD | |
| A(-4, 6, 3) | (3, -5, 1) | (2, 6, -4) | D(2, 4, -5) | ACD | |
| A(7, 5, 8) | (-4, -5, 3) | (2, -3, 5) | D(5, 1, -4) | BCD | |
| A(3, -2, 6) | (-6, -2, 3) | (1, 1, -4) | D(4, 6, -7) | ABD | |
| A(-5, -4, -3) | (7, 3, -1) | (6, -2, 0) | D(3, 2, -7) | BCD | |
| A(3, -5, -2) | (-4, 2, 3) | (1, 5, 7) | D(-2,-4, 5) | ACD | |
| (7, 4, 9) | (1, -2, -3) | (-5, -3, 0) | D(1, -3, 4) | ABD | |
| A(-4, -7, -3) | (-4, -5, 7) | (2, -3, 3) | D(3, 2, 1) | BCD | |
| (-4, -5, -3) | (3, 1, 2) | (5, 7, -6) | D(6, -1, 5) | ACD | |
| A(5, 2, 4) | (-3, 5, -7) | (1, -5, 8) | D(9, -3, 5) | ABD | |
| A(-6, 4, 5) | (5, -7, 3) | (4, 2, -8) | D(2, 8, -3) | ACD | |
| A(5, 3, 6) | (-3, -4, 4) | (5, -6, 8) | D(4, 0, -3) | BCD | |
| A(5, -4, 4) | (-4, -6, 5) | (3, 2, -7) | D(6, 2, -9) | ABD | |
| A(-7, -6, -5) | (5, 1, -3) | (8, -4, 0) | D(3, 4, -7) | BCD | |
| A(7, -1, -2) | (1, 7, 8) | (3, 7, 9) | D(-3, -5, 2) | ACD | |
| A(5, 2, 7) | (7, -6, -9) | (-7, -6, 3) | D(l, -5, 2) | ABD | |
| A(-2, -5, -1) | (-6, -7, 9) | (4, -5, 1) | D(2, 1, 4) | BCD | |
| A(-6, -3, -5) | (5, 1, 7) | C(3, 5, -1) | D(4, -2, 9) | ACD | |
| A(7, 4, 2) | B(-5, 3, -9) | C(1, -5, 3) | D(7, -9, 1) | AD | |
| A(-8, 2, 7) | B(3, -5, 9) | (2, 4, -6) | D(4, 6, -5) | AD | |
| A(4, 3, 1) | (2, 7, 5) | (-4, -2, 4) | D(2, -3, -5) | ACD | |
| A(-9, -7, 4) | B(-4, 3, -1) | (5, -4, 2) | D(3, 4, 4) | BCD | |
| A(3, 5, 3) | (-3, 2, 8) | (-3, -2, 6) | D(7, 8, -2) | ACD | |
| A(4, 2, 3) | B(-5, -4, 2) | (5, 7, -4) | D(6, 4, -7) | ABD | |
| A(-4, -2, -3) | (2, 5, 7) | (6, 3, -1) | D(6, -4, 1) | ACD |
|
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|
1. = 4i + 4k, b = -i + 3j + 2k = = 3i + 5j. :
) a, b 5;
) 3 b;
) 3b;
) , b;
) , a, b .
) 5 = 15i + 25j,
= -100-180-200 = -480;
) 3 = 9i + 15j,
= 30i + 27k +15k 18j = 30i 18j + 42k,
= 
;
) : 3b = -3i + 9j + 6k, 
= 4(-3) + 0 + 24 =12;
) 
= (4, 0, 4), 
= (-1, 3, 2) 
, .
,
;
) , b, , abc = 0.
abc = 
= -20-36-40 ≠ 0,
. . a, b .
2. (2, 3, 4), B(4, 7, 3), (1, 2, 2) D(-2, 0, -1). :
) ABC;
) ABCD.
) , SABC = 
|AB×AC|. : 
= (2, 4, -1), 
= (-1, -1, -2),
AB×AC = 
= -9i+5j+2k.
:
SABC = 
= 
;
) V = 
| 
|; 
= (-4,-3,-5),
= 
= 11.
.
1) , ?
2) ?
3) ?
4) ?
