If \[\mathbf{a,}\,\mathbf{b,}\,\mathbf{c}\] are non-coplanar vectors and \[\mathbf{d}=\lambda \mathbf{a}+\mu \,\mathbf{b}+\nu \mathbf{c},\] then \[\lambda \] is equal to [Roorkee 1999]

\[\frac{[\mathbf{b}\,\mathbf{d}\,\mathbf{c}]}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\]

\[\frac{[\mathbf{d}\,\mathbf{b}\,\mathbf{c}]}{[\mathbf{b}\,\mathbf{a}\,\mathbf{c}]}\]

\[\frac{[\mathbf{b}\,\mathbf{c}\,\mathbf{d}]}{[\mathbf{b}\,\mathbf{c}\,\mathbf{a}]}\]

\[\frac{[\mathbf{c}\,\mathbf{b}\,\mathbf{d}\,]}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\]

If \[\mathbf{a,}\,\mathbf{b,}\,\mathbf{c}\] are non-coplanar vectors a

1.	If \[\mathbf{a,}\,\mathbf{b,}\,\mathbf{c}\] are non-coplanar vectors and \[\mathbf{d}=\lambda \mathbf{a}+\mu \,\mathbf{b}+\nu \mathbf{c},\] then \[\lambda \] is equal to [Roorkee 1999]
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.	\[\frac{[\mathbf{c}\,\mathbf{b}\,\mathbf{d}\,]}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\]
Answer» C. \[\frac{[\mathbf{b}\,\mathbf{d}\,\mathbf{c}]}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\]

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If \[\mathbf{a,}\,\mathbf{b,}\,\mathbf{c}\] are non-coplanar vectors and \[\mathbf{d}=\lambda \mathbf{a}+\mu \,\mathbf{b}+\nu \mathbf{c},\] then \[\lambda \] is equal to [Roorkee 1999]

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