Unit vectors a, b and c are coplanar. A unit vector d is perpendicular to them. If \[(\mathbf{a}\times \mathbf{b})\times (\mathbf{c}\times \mathbf{d})=\frac{1}{6}\mathbf{i}-\frac{1}{3}\mathbf{j}+\frac{1}{3}\mathbf{k}\] and the angle between a and b is \[{{30}^{o}}\], then c is [Roorkee Qualifying 1998]

\[\frac{(2\mathbf{i}+\mathbf{j}-\mathbf{k})}{3}\]

\[\frac{(\mathbf{i}-2\mathbf{j}+2\mathbf{k})}{3}\]

\[\frac{(-\mathbf{i}+2\mathbf{j}-2\mathbf{k})}{3}\]

\[\frac{(-\mathbf{i}+2\mathbf{j}+\mathbf{k})}{3}\]

Unit vectors a, b and c are coplanar. A unit vector d is perpendicular

1.	Unit vectors a, b and c are coplanar. A unit vector d is perpendicular to them. If \[(\mathbf{a}\times \mathbf{b})\times (\mathbf{c}\times \mathbf{d})=\frac{1}{6}\mathbf{i}-\frac{1}{3}\mathbf{j}+\frac{1}{3}\mathbf{k}\] and the angle between a and b is \[{{30}^{o}}\], then c is [Roorkee Qualifying 1998]
A.	\[\frac{(\mathbf{i}-2\mathbf{j}+2\mathbf{k})}{3}\]
B.	\[\frac{(2\mathbf{i}+\mathbf{j}-\mathbf{k})}{3}\]
C.	\[\frac{(-\mathbf{i}+2\mathbf{j}-2\mathbf{k})}{3}\]
D.	\[\frac{(-\mathbf{i}+2\mathbf{j}+\mathbf{k})}{3}\]
Answer» B. \[\frac{(2\mathbf{i}+\mathbf{j}-\mathbf{k})}{3}\]

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