Triple Product

Given three vectors the program calculates the triple product. Its magnitude is equal to the volume of the parallelepiped formed by the three vectors.

Linearly dependent vectors have a triple product of zero, because they lie in one plane

Example 1:


->  ⎧ 2 ⎫     ->  ⎧ 2 ⎫    ->  ⎧ 3 ⎫
a = ⎪ 3 ⎪     b = ⎪-1 ⎪    c = ⎪ 9 ⎪
    ⎩ 5 ⎭         ⎩ 7 ⎭        ⎩ 2 ⎭

  ->  ->    ->  
( a x b ) · c = 26

Example 2:


->  ⎧ 1 ⎫     ->  ⎧ 2 ⎫    ->  ⎧-1 ⎫
a = ⎪ 2 ⎪     b = ⎪ 1 ⎪    c = ⎪ 4 ⎪
    ⎩ 1 ⎭         ⎩ 1 ⎭        ⎩ 1 ⎭

  ->  ->    ->  
( a x b ) · c = 0

The three vectors are linearly dependent.

See also:

Wikipedia: Triple product