A) \[\frac{[\mathbf{d}\,\mathbf{b}\,\mathbf{c}]}{[\mathbf{b}\,\mathbf{a}\,\mathbf{c}]}\]
B) \[\frac{[\mathbf{b}\,\mathbf{c}\,\mathbf{d}]}{[\mathbf{b}\,\mathbf{c}\,\mathbf{a}]}\]
C) \[\frac{[\mathbf{b}\,\mathbf{d}\,\mathbf{c}]}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\]
D) \[\frac{[\mathbf{c}\,\mathbf{b}\,\mathbf{d}\,]}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\]
Correct Answer: B
Solution :
Since \[d=\lambda a+\mu b+\nu c\] \\[d.(b\times c)=\lambda \,a.(b\times c)+\mu \,b.(b\times c)+\mu \,c.(b\times c)\] \[=\lambda \left[ a\,b\,c \right]\] Þ \[\lambda =\frac{[d\,b\,c]}{[a\,b\,c]}\]\[=\frac{[b\,c\,d]}{[b\,c\,a]}\].b
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