Prove that: `[vecaxxvecb vecb xx vecc veccxxveca]=[vecavecbvecc]^2`

Explanation

To prove the equation \([ \vec{A} \times \vec{B}, \vec{B} \times \vec{C}, \vec{C} \times \vec{A} ] = [ \vec{A}, \vec{B}, \vec{C} ]^2\), we will follow these steps:

### Step 1: Understand the Scalar Triple Product
The scalar triple product of three vectors \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\) is given by:
\[ [\vec{A}, \vec{B}, \vec{C}] = \vec{A} \cdot (\vec{B} \times \vec{C}) \]
This represents the volume of the parallelepiped formed by the three vectors.
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