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.