Prove that `(veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vecbxxhatk))hatk=vecaxxvecb`

Explanation

To prove that

\[ (\vec{a} \cdot (\vec{b} \times \hat{i})) \hat{i} + (\vec{a} \cdot (\vec{b} \times \hat{j})) \hat{j} + (\vec{a} \cdot (\vec{b} \times \hat{k})) \hat{k} = \vec{a} \times \vec{b} \]

we will break down the left-hand side step by step.

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