A) \[(\mathbf{a}\times \mathbf{a})\,.\,(\mathbf{b}\times \mathbf{b})\]
B) \[(\mathbf{a}\,.\,\mathbf{a})\,(\mathbf{b}\,.\,\mathbf{b})\]
C) \[|\,(\mathbf{a}\times \mathbf{b})\,|\,\,(\mathbf{a}\,.\,\mathbf{b})\]
D) \[2\,(\mathbf{a}\,.\,\mathbf{b})\,(\mathbf{a}\,.\,\mathbf{b})\]
Correct Answer: B
Solution :
We know \[{{(\mathbf{a}\times \mathbf{b})}^{2}}+{{(\mathbf{a}\,.\,\mathbf{b})}^{2}}={{a}^{2}}{{b}^{2}}=(\mathbf{a}\,.\,\mathbf{a})(\mathbf{b}\,.\,\mathbf{b})\].
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