A) \[2(\,\mathbf{a}\times \mathbf{b})\]
B) \[\mathbf{a}\times \mathbf{b}\]
C) \[{{a}^{2}}-{{b}^{2}}\]
D) None of these
Correct Answer: A
Solution :
\[(\mathbf{a}-\mathbf{b})\times (\mathbf{a}+\mathbf{b})=\mathbf{a}\times \mathbf{a}-\mathbf{b}\times \mathbf{a}+\mathbf{a}\times \mathbf{b}-\mathbf{b}\times \mathbf{b}\] \[=\mathbf{a}\times \mathbf{b}-\mathbf{b}\times \mathbf{a}=\mathbf{a}\times \mathbf{b}+\mathbf{a}\times \mathbf{b}=2(\mathbf{a}\times \mathbf{b}).\]
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