A) \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{5}{\sqrt{3}} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{\sqrt{5}}{3} \right)\]
Correct Answer: D
Solution :
\[\cos \theta =\frac{\vec{A}\vec{B}}{AB}=\frac{42+24-12}{\sqrt{36+36+9}\sqrt{49+16+16}}\]\[=\frac{56}{9\sqrt{71}}\] \[\cos \theta =\frac{56}{9\sqrt{71}}\] \ \[\sin \theta =\frac{\sqrt{5}}{3}\] or \[\theta ={{\sin }^{-1}}\left( \frac{\sqrt{5}}{3} \right)\]
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