Let `veca, vecb , vecc` be non -coplanar vectors and let equations `veca', vecb', vecc'` are reciprocal system of vector `veca, vecb ,vecc` then prove that `veca xx veca' + vecb xx vecb' + vecc xx vecc'` is a null vector.

Explanation

To prove that \(\vec{a} \times \vec{a}' + \vec{b} \times \vec{b}' + \vec{c} \times \vec{c}'\) is a null vector, we start with the definitions of the reciprocal vectors.

### Step 1: Define the reciprocal vectors
Given that \(\vec{a}', \vec{b}', \vec{c}'\) are the reciprocal system of the vectors \(\vec{a}, \vec{b}, \vec{c}\), we can express them as:
\[ \vec{a}' = \frac{\vec{b} \times \vec{c}}{|\vec{a}, \vec{b}, \vec{c}|}, \quad \vec{b}' = \frac{\vec{c} \times \vec{a}}{|\vec{a}, \vec{b}, \vec{c}|}, \quad \vec{c}' = \frac{\vec{a} \times \vec{b}}{|\vec{a}, \vec{b}, \vec{c}|} \]
where \(|\vec{a}, \vec{b}, \vec{c}|\) denotes the scalar triple product.
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