A) \[{{\sin }^{-1}}\left( \frac{1}{7} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{2}{7} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{1}{7} \right)\]
D) None of these
Correct Answer: C
Solution :
Angle between two lines, \[\cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\] \[\therefore \,\,\,\cos \theta =\frac{1\times 3+2\times -2+3\times 1}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}\sqrt{{{3}^{2}}+{{(-2)}^{2}}+{{1}^{2}}}}\]\[=\frac{2}{\sqrt{14}\sqrt{14}}\] \[\therefore \,\,\theta ={{\cos }^{-1}}\left( \frac{1}{7} \right)\].
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