## 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.