A) 0
B) 2
C) ? 2
D) None of these
Correct Answer: A
Solution :
\[\frac{\mathbf{a}.\mathbf{b}\times \mathbf{c}}{\mathbf{c}\times \mathbf{a}.\mathbf{b}}+\frac{\mathbf{b}.\mathbf{a}\times \mathbf{c}}{\mathbf{c}.\mathbf{a}\times \mathbf{b}}=\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{[\mathbf{c}\,\mathbf{a}\,\mathbf{b}]}+\frac{[\mathbf{b}\,\mathbf{a}\,\mathbf{c}]}{[\mathbf{c}\,\mathbf{a}\,\mathbf{b}]}=\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{[\mathbf{c}\,\mathbf{a}\,\mathbf{b}]}-\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{[\mathbf{c}\,\mathbf{a}\,\mathbf{b}]}=0.\]
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