Let \[\mathbf{a}=2\mathbf{i}-\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=\mathbf{i}+2\mathbf{j}-\mathbf{k}\] and \[\mathbf{c}=\mathbf{i}+\mathbf{j}-2\mathbf{k}\] be three vectors. A vector in the plane of b and c whose projection on a is of magnitude \[\sqrt{2/3}\] is [IIT 1993; Pb. CET 2004]

\[2\mathbf{i}+3\mathbf{j}+3\mathbf{k}\]

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

\[-\,2\mathbf{i}-\mathbf{j}+5\mathbf{k}\]

\[2\mathbf{i}+\mathbf{j}+5\mathbf{k}\]

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 \[\mathbf{c}=\mathbf{i}+\mathbf{j}-2\mathbf{k}\] be three vectors. A vector in the plane of b and c whose projection on a is of magnitude \[\sqrt{2/3}\] is [IIT 1993; Pb. CET 2004]
A.	\[2\mathbf{i}+3\mathbf{j}-3\mathbf{k}\]
B.	\[2\mathbf{i}+3\mathbf{j}+3\mathbf{k}\]
C.	\[-\,2\mathbf{i}-\mathbf{j}+5\mathbf{k}\]
D.	\[2\mathbf{i}+\mathbf{j}+5\mathbf{k}\]
Answer» B. \[2\mathbf{i}+3\mathbf{j}+3\mathbf{k}\]

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