A) \[{{\cos }^{-1}}\left( \frac{17}{21} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{18}{21} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{20}{21} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{23}{21} \right)\]
Correct Answer: C
Solution :
Let \[\theta \] be the angle between two lines whose direction ratios be \[\left( 2,3,6 \right)\] and\[\left( 1,2,2 \right)\]. \[\therefore \cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}.\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}=\frac{2\times 1+3\times 2+6\times 2}{\sqrt{49}.\sqrt{9}}=\frac{20}{7\times 3}=\frac{20}{21}\] \[\therefore \theta ={{\cos }^{-1}}\left( \frac{20}{21} \right)\] Hence, option is correct.
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