|
|
|
(a1, a2, a3)
| =
|
a1i + a2j + a3k
| (basis i, j, k)
|
|
(a1,a2,a3) .
(b1,b2,b3)
| =
|
a1b1 +
a2b2 +
a3b3
| ("dot product",
& other dimensions)
|
|
(a1,a2,a3) ×
(b1,b2,b3)
| =
|
(a2b3-a3b2,
a3b1-a1b3,
a1b2-a2b1)
| (3D "cross product")
|
|
| =
|
| | |
i | j | k |
| |
| | |
a1 | a2 | a3 |
| |
| | |
b1 | b2 | b3 |
| |
| (as a determinant)
|
|
|