A) \[{{\cos }^{-1}}\frac{2}{\sqrt{7}}\]
B) \[{{\sin }^{-1}}\frac{2}{\sqrt{7}}\]
C) \[{{\cos }^{-1}}\frac{2}{\sqrt{5}}\]
D) \[{{\sin }^{-1}}\frac{2}{\sqrt{5}}\]
Correct Answer: B
Solution :
\[\cos \theta =\frac{3(2)+(1)(-2)+2(4)}{\sqrt{9+1+4}\sqrt{4+4+16}}\]\[=\frac{12}{\sqrt{14}\sqrt{24}}=\frac{6}{\sqrt{14}\sqrt{6}}\] \[\Rightarrow \cos \theta =\frac{\sqrt{3}}{\sqrt{7}}\Rightarrow \sin \theta =\frac{2}{\sqrt{7}}\] Þ \[\theta ={{\sin }^{-1}}\left( \frac{2}{\sqrt{7}} \right)\].
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