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.
-> | 1 | -> | 7 | a = | 2 | b = | 1 | | 3 | | 4 | -> -> | 5 | -> -> a x b = | 17 | |a x b|= 21,977261 |-13 |
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.