## Vector Product

Given two vectors the vector product and its magnitude are calculated.

The vector product is a vector orthogonal to the parallelogram which is put up
by the given vectors. Its magnitude is equal to the area of the parallelogram.

### Example:

`
-> ⎧ 1 ⎫ -> ⎧ 7 ⎫
a = ⎪ 2 ⎪ b = ⎪ 1 ⎪
⎩ 3 ⎭ ⎩ 4 ⎭
-> -> ⎧ 5 ⎫ -> ->
a x b = ⎪ 17 ⎪ |a x b|= 21,977261
⎩-13 ⎭`

### Application:

Assume the area of the triangle with corners A(0|0|0), B(1|2|3) and C(7|1|4) is to be calculated.

The triangle is half of the parallelogram that is spanned by the two vectors in the example.
Its area is therefore half of their vector product A ≈ 11 FE.

### See also:

Wikipedia: Cross product