A) \[{{\cos }^{-1}}\left( \frac{2}{7\sqrt{6}} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{1}{7\sqrt{6}} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{3}{7\sqrt{6}} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{5}{7\sqrt{6}} \right)\]
Correct Answer: A
Solution :
\[\theta ={{\cos }^{-1}}\left[ \frac{(1)(2)+(2)(-3)+(1)(6)}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{1}^{2}}}\sqrt{{{2}^{2}}+{{(-3)}^{2}}+{{6}^{2}}}} \right]\] \[{{\cos }^{-1}}\,\left[ \frac{2-6+6}{\sqrt{6}\sqrt{49}} \right]={{\cos }^{-1}}\left[ \frac{2}{7\sqrt{6}} \right]\].
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