question_answer

If the vectors \[\overrightarrow{a}=\hat{i}-\hat{j}+2\hat{k},\] \[\overrightarrow{b}=2\hat{i}+4\hat{j}+\hat{k}\] and \[\overrightarrow{c}=\lambda \hat{i}+\hat{j}+\mu \hat{k}\] are mutually orthogonal, then \[(\lambda ,\mu )\] is equal to

A)  \[(-3,\,2)\]

B)  \[(2,-3)\]

C)  \[(-2,3)\]                       

D)  \[(3,-2)\]

E)  None of these