## Vector Product

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

The vector product is a vector orthogonal to the parallelogram formed 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:

Suppose you want to calculate the area of the triangle with vertices A(0|0|0), B(1|2|3) and C(7|1|4).

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 area units.