Задачи по аналитической геометрии. Микенберг М.А. - 32 стр.

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{
~
i,
~
j,
~
k} ~a(x
1
; y
1
; z
1
)
~
b(x
2
; y
2
; z
2
) ~c(x
3
; y
3
; z
3
)
[~a,
~
b] =
¯
¯
¯
¯
¯
¯
~
i
~
j
~
k
x
1
y
1
z
1
x
2
y
2
z
2
¯
¯
¯
¯
¯
¯
, (~a,
~
b,~c) =
¯
¯
¯
¯
¯
¯
x
1
y
1
z
1
x
2
y
2
z
2
x
3
y
3
z
3
¯
¯
¯
¯
¯
¯
.
~a(2; 2; 1)
~
b(2; 3; 6)
~a(3; 1; 0)
~
b(4; 5; 6)
A(1; 2; 0) B(3; 0; 3) C(5; 2; 6)
ABC
A(1; 1; 2) B(5, 6, 2) C(1, 3 1)
B AC
~x ~a(2; 3; 1)
~
b(1; 2; 3) (~x,
~
i + 2
~
j 7
~
k) = 10
~a(1; 1; 3)
~
b(2; 2; 1) ~c(3; 2; 5)
(~a,
~
b,~c)
~a(2; 3; 1)
~
b(1; 1; 3) ~c(1; 9; 11)
~a(3; 2; 1)
~
b(2; 1; 2) ~c(3; 1; 2)
~a(2; 1; 2)
~
b(1; 2; 3) ~c(3; 4; 7)
A(1; 2 1) B(0; 1; 5) C(1; 2; 1)
D(2; 1; 3)
A(2; 1; 1) B(5; 5; 4) C(3; 2; 1) D(4; 1; 3)
A(2; 3; 1) B(4; 1; 2) C(6; 3; 7)
D(5; 4; 8) D
5
A(2; 1 1) B(3; 0; 1) C(2; 1; 3)
OY
~a(2; 3; 1)
~
b(3; 1; 2) ~c(1; 2; 3) [[~a,
~
b],~c]
[~a, [
~
b,~c]]
A
(2;
1;
3) B
(1; 2;
4) C
(3;
1;
2)