A) \[{{\cos }^{-1}}\left( \frac{1}{9} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{2}{9} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{3}{9} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{4}{9} \right)\]
Correct Answer: D
Solution :
\[\theta ={{\cos }^{-1}}\,\left( \frac{(2)\,(1)+(2)\,(2)\,+(-1)\,(2)}{\sqrt{{{2}^{2}}+{{2}^{2}}+{{1}^{2}}}\sqrt{{{1}^{2}}+{{2}^{2}}+{{2}^{2}}}} \right)={{\cos }^{-1}}\frac{4}{9}\].
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