.
http://ua.onlinemschool.com/math/assistance/vector/multiply1/
a
b
,
a
b
.
a
b
, .
. , .
a
=
{ax
;
ay}
b
=
{bx
;
by}
a
b
=
ax bx
+
ay by
1.
a
=
{
1; 2
}
b
=
{
4; 8
}
.
'
a
b
= 1 4 + 2 8 = 4 + 16 = 20
a
=
{ax
;
ay
;
az}
b
=
{bx
;
by
;
bz}
a
b
=
ax bx
+
ay by
+
az bz
1.
a
=
{
1; 2; -5
}
b
=
{
4; 8; 1
}
.
'
a
b
= 1 4 + 2 8 + (-5) 1 = 4 + 16 - 5 = 15
.
http://ua.onlinemschool.com/math/assistance/vector/multiply1/
a
=
{x1; y1; z1}
b
=
{x2; y2; z2}
- :
| a × b = | i | j | k | = i(y1z2 - z1y2) - j(x1z2 - z1x2) + k(x1y2 - y1x2) |
| x1 | y1 | z1 | ||
| x2 | y2 | z2 |
a
×
b
=
{y1 z2 - z1 y2; z1 x2 - x1 z2; x1 y2 - y1 x2}
1.
a
b
.
2.
a
b
.
1.
a
=
{
1; 2; 3
}
b
=
{
2; 1; -2
}
.
'
| a × b = | i | j | k | = |
| -2 |
=
I
(2 (-2) - 3 1) -
J
(1 (-2) - 2 3) +
K
(1 1 - 2 2) =
{
-7; 8; -3
}
.
http://ua.onlinemschool.com/math/assistance/vector/multiply2/
̳
a
b
c
.
̳ , .
1. ' , .
2.
a
[
b
×
c
] =
b
[
c
×
a
] =
c
[
a
×
b
] = -
a
[
c
×
b
] = -
b
[
a
×
c
] = -
c
|
|
|
[
b
×
a
]
3. , .
1.
a
=
{
1; 2; 3
}
,
b
=
{
1; 1; 1
}
,
c
=
{
1; 2; 1
}
.
':
| a [ b × ] = | = | |||
= 111 + 112 + 123 - 113 - 112 - 112 = 1 + 2 + 6 - 3 - 2 - 2 = 2
.
- , , , .
- , , .
a
=
{ax
;
ay}
b
a
b
=
{ax b
;
ay b}
1.
a
=
{
1; 2
}
3.
'
3
a
=
{
3 1; 3 2
}
=
{
3; 6
}
a
=
{ax
;
ay
;
az}
b
a
b
=
{ax b
;
ay b
;
az b}
1.
a
=
{
1; 2; -5
}
2.
'
2
a
=
{
2 1; 2 2; 2 (-5)
}
=
{
2; 4; -10
}
.
( )
a
+
b
-
c
, ,
a
b
,
c
:
i
=
ai
+
bi
г ( )
a
-
b
-
c
, ,
a
b
,
c
:
i
=
ai - bi
a
=
{ax
;
ay}
b
=
{bx
;
by}
a
+
b
=
{ax
+
bx
;
ay
+
by}
a
-
b
=
{ax - bx; ay - by}
1.
a
=
{
1; 2
}
b
=
{
4; 8
}
.
'
a
+
b
=
{
1 + 4; 2 + 8
}
=
{
5; 10
}
2.
a
=
{
1; 2
}
b
=
{
4; 8
}
.
'
a
+
b
=
{
1 - 4; 2 - 8
}
=
{
-3; -6
}
a
=
{ax
;
ay
;
az}
b
=
{bx
;
by
;
bz}
a
+
b
=
{ax
+
bx
;
ay
+
by
;
az
+
bz}
a
-
b
=
{ax - bx; ay - by; az - bz}
1.
a
=
{
1; 2; 5
}
b
=
{
4; 8; 1
}
.
'
a
+
b
=
{
1 + 4; 2 + 8; 5 + 1
}
=
{
5; 10; 6
}
2.
a
=
{
1; 2; 5
}
b
=
{
4; 8; 1
}
.
'
a
+
b
=
{
1 - 4; 2 - 8; 5 - 1
}
=
{
-3; -6; 4
}
.
, . , . .
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|
|
. 
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