MatheAss 9.0Linear Algebra

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
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