A) \[{{\sin }^{-1}}\left( \frac{3}{13} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{4}{13} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{4}{13} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{3}{13} \right)\]
Correct Answer: C
Solution :
The angle subtended by the vector \[\text{\vec{A}}\]with the x-axis is \[\cos \theta =\frac{4}{\sqrt{{{4}^{2}}+{{3}^{2}}+{{(12)}^{2}}}}=\frac{4}{13};\] \[\cos \theta ={{\cos }^{-1}}\left( \frac{4}{13} \right)\]
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