A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{2}\]
C) \[{{\cos }^{-1}}\left( \frac{2}{225} \right)\]
D) \[\frac{\pi }{4}\]
E) \[\frac{\pi }{6}\]
Correct Answer: A
Solution :
\[\because \] \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0\] \[\Rightarrow \] \[{{(\overrightarrow{a}+\overrightarrow{b})}^{2}}={{(-\overrightarrow{c})}^{2}}\] \[\Rightarrow \] \[|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}+2|\overrightarrow{a}||\overrightarrow{b}|\cos \theta =|\overrightarrow{c}{{|}^{2}}\] \[\Rightarrow \] \[9+25+2\times 3\times 5\cos \theta =49\] \[\Rightarrow \] \[\cos \theta =\frac{15}{30}=\frac{1}{2}\] \[\Rightarrow \] \[\theta =\frac{\pi }{3}\]
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