question_answer

Let \[\overrightarrow{a}=\hat{i}+2\hat{j}+\hat{k},\] \[\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k}\] and \[\overrightarrow{c}=\hat{i}+\hat{j}-\hat{k}\]. A vector in the plane of \[\overrightarrow{a}\] and \[\overrightarrow{b}\] whose projection on \[\overrightarrow{c}\] is \[\frac{1}{\sqrt{3}},\]is

A)  \[4\hat{i}-\hat{j}+4\hat{k}\]     

B)  \[3\hat{i}+\hat{j}-3\hat{k}\]

C)  \[2\hat{i}+\hat{j}-2\hat{k}\]                 

D)  \[4\hat{i}+\hat{j}-4\hat{k}\]

E)  None of these