Question: Prove the following vector identities: a. ((mathbf{a} times mathbf{b}) cdot(mathbf{c} times mathbf{d})=(mathbf{a} cdot mathbf{c})(mathbf{b} cdot mathbf{d})-(mathbf{a} cdot mathbf{d})(mathbf{b} cdot mathbf{c})). b. ((mathbf{a} times mathbf{b}) times(mathbf{c}

Prove the following vector identities:

a. $(\mathbf{a} \times \mathbf{b}) \cdot(\mathbf{c} \times \mathbf{d})=(\mathbf{a} \cdot \mathbf{c})(\mathbf{b} \cdot \mathbf{d})-(\mathbf{a} \cdot \mathbf{d})(\mathbf{b} \cdot \mathbf{c})$.

b. $(\mathbf{a} \times \mathbf{b}) \times(\mathbf{c} \times \mathbf{d})=(\mathbf{a} \cdot \mathbf{b} \times \mathbf{d}) \mathbf{c}-(\mathbf{a} \cdot \mathbf{b} \times \mathbf{c}) \mathbf{d}$.

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