Prove that `hati xx(vecaxxveci)+hatjxx(vecaxxvecj)+hatkxx(vecaxxveck)=2veca`

Explanation

To prove that \( \hat{i} \times (\vec{a} \times \hat{i}) + \hat{j} \times (\vec{a} \times \hat{j}) + \hat{k} \times (\vec{a} \times \hat{k}) = 2\vec{a} \), we will follow these steps:

### Step 1: Write down the left-hand side (LHS)
The LHS is:
\[ \hat{i} \times (\vec{a} \times \hat{i}) + \hat{j} \times (\vec{a} \times \hat{j}) + \hat{k} \times (\vec{a} \times \hat{k}) \]

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