A) \[{{\tan }^{-1}}\sqrt{8}\]
B) \[{{\tan }^{-1}}\sqrt{3}\]
C) \[{{\tan }^{-1}}\sqrt{10}\]
D) \[{{\tan }^{-1}}\sqrt{2}\]
Correct Answer: C
Solution :
Vector\[\text{\vec{V}}\]along the line of intersection of the given planes is \[\text{\vec{V}=}\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 2 & 1 & 1 \\ 1 & 1 & 2 \\ \end{matrix} \right|=\hat{i}(2-1)-\hat{j}(4-1)+\hat{k}(2-1)\] \[=\hat{i}-3\hat{j}+\hat{k}\] \[\vec{u}=\hat{i},\therefore \cos \theta =\frac{1}{\sqrt{11}};\theta ={{\tan }^{-1}}\sqrt{10}\]
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