Let \[\mathbf{a}=2\mathbf{i}+\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=\mathbf{i}+2\mathbf{j}-\mathbf{k}\]and a unit vector c be coplanar. If c is perpendicular to a, then c = [IIT 1999; Pb. CET 2003; DCE 2005]

\[\frac{1}{\sqrt{3}}(-\mathbf{i}-\mathbf{j}-\mathbf{k})\]

\[\frac{1}{\sqrt{2}}(-\mathbf{j}+\mathbf{k})\]

\[\frac{1}{\sqrt{5}}\,(\mathbf{i}-2\mathbf{j})\]

\[\frac{1}{\sqrt{3}}(\mathbf{i}-\mathbf{j}-\mathbf{k})\]

Let \[\mathbf{a}=2\mathbf{i}+\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=\mat

1.	Let \[\mathbf{a}=2\mathbf{i}+\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=\mathbf{i}+2\mathbf{j}-\mathbf{k}\]and a unit vector c be coplanar. If c is perpendicular to a, then c = [IIT 1999; Pb. CET 2003; DCE 2005]
A.	\[\frac{1}{\sqrt{2}}(-\mathbf{j}+\mathbf{k})\]
B.	\[\frac{1}{\sqrt{3}}(-\mathbf{i}-\mathbf{j}-\mathbf{k})\]
C.	\[\frac{1}{\sqrt{5}}\,(\mathbf{i}-2\mathbf{j})\]
D.	\[\frac{1}{\sqrt{3}}(\mathbf{i}-\mathbf{j}-\mathbf{k})\]
Answer» B. \[\frac{1}{\sqrt{3}}(-\mathbf{i}-\mathbf{j}-\mathbf{k})\]

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Let \[\mathbf{a}=2\mathbf{i}+\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=\mathbf{i}+2\mathbf{j}-\mathbf{k}\]and a unit vector c be coplanar. If c is perpendicular to a, then c = [IIT 1999; Pb. CET 2003; DCE 2005]

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