for any four vectors `veca,vecb, vecc and vecd` prove that `vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]`

Explanation

To prove the equation \( \vec{d} \cdot (\vec{a} \times (\vec{b} \times (\vec{c} \times \vec{d}))) = (\vec{b} \cdot \vec{d}) [\vec{a} \, \vec{c} \, \vec{d}] \), we will start with the left-hand side (LHS) and manipulate it step by step to show that it equals the right-hand side (RHS).

### Step 1: Start with the LHS
We start with the left-hand side:
\[ \vec{LHS} = \vec{d} \cdot (\vec{a} \times (\vec{b} \times (\vec{c} \times \vec{d}))) \]

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