Векторная алгебра

r

r

r

ax

a y

az

a

b c =

bx

by

bz

.

(21)

cx

cy

cz

1.15. / !&. ( "

3 ". * ,

r

r r

,

r

a

, b , c

a = k ,

r

r

b = i ,

c = j .

/.

r

0

1

r

r

0

1 0 0

= 1 > 0 .

a

b

c =

0

1

0

r

' 6

- *

r

r

a, b , c

*.

!: * .

3 ". ' "

+

*

,

- *

:

A(− 1;−3;1),

B(3;3;−2), C (− 1; 4; 2), D(0;0; 5).

/. AB = (4; 6;− 3),

AC = (0; 7;1),

AD = (1; 3; 4),

6

− 3

4

V =

1

AB AC AD

=

1

0

7

1

=

1

127 =

127

.

6

6

6

6

1

3

4

) A(3; 2; −1),

B(1;2 ; −2), C (− 1; 0;1),

D(1;1;1),

) A(− 2; 0;1),

B(3;1; 2), C (0;−1; 3),

D(1; 2; 0).

) AB = (− 2; 0; −1);

AC = (− 4; −2; 2);

AD = (− 2; −1; 2);

− 2

0

− 1

AB AC AD =

− 4

− 2

2

= 4 ≠ 0 .

− 2

− 1

2

41

) AB = (5;1;1);

AC = (2; −1; 2);

AD = (3; 2; −1);

1

1

5

AB AC AD =

2 − 1

2

= 0 .

3

2

− 1

3 " A, B, C, D " *.

!: ) ; ) .

1.16. 3 " #$# + &

,

r

r

,

* a

, b, c

)

r

= (2; 3; − 1);

b = (1; −1; 3);

r

=

(1; 9; −11);

a

c

)

r

= (3 ;−2;1);

b = (2;1; 2);

r

=

(3; −1; −2).

a

c

' " +

/, - ( " (

A(2 ;−1;1), B(5; 5; 4),

C (3; 2;1) D(4;1; 3) (

* ).

''2%21 2...........................................................................................................

3

1. ) &68 1:2 '2 3 1:2 '26 # 1:...............................................

4

4 46 $ & #2) ; )! ) ...............................................................

47