A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
Correct Answer: C
Solution :
Given, \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\]and \[|\vec{a}|=\sqrt{37},|\vec{b}|\,=3\] and \[|\vec{c}|=4\] \[\therefore \] \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\] \[\Rightarrow \] \[\vec{a}=-(\vec{b}+\vec{c})\] \[\Rightarrow \] \[|\vec{a}{{|}^{2}}=|-\vec{b}+\vec{c}{{|}^{2}}\] \[\Rightarrow \]\[|\vec{a}{{|}^{2}}=|\vec{b}{{|}^{2}}+|\vec{c}{{|}^{2}}+\,2|\vec{b}||\vec{c}|cos\theta \] \[=9+16+24\cos \theta \] \[\Rightarrow \] \[37=25+24\cos \theta \] \[\Rightarrow \] \[24\cos \theta =12\] \[\Rightarrow \] \[\theta ={{60}^{o}}.\]
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