If vectors, `vecb, vecc and vecd` are not coplanar, the prove that vector `(veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) ` is parallel to `veca`.

Explanation

To prove that the vector expression

\[ \vec{a} \times (\vec{b} \times (\vec{c} \times \vec{d})) + (\vec{a} \times (\vec{c} \times (\vec{d} \times \vec{b}))) + (\vec{a} \times (\vec{d} \times (\vec{b} \times \vec{c}))) \]

is parallel to \(\vec{a}\), we will use the vector triple product identity.

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