Linear Algebra

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.

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