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