A) \[{{120}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{150}^{o}}\]
Correct Answer: D
Solution :
Given that, \[|\vec{a}|=3\sqrt{3},\] \[|\vec{b}|=4\]and \[|\vec{a}+\vec{b}|=\sqrt{7}\] Now, \[|\vec{a}+\vec{b}{{|}^{2}}=|\vec{a}{{|}^{2}}+|\vec{b}{{|}^{2}}+2|\vec{a}||\vec{b}|\cos \theta \] \[\Rightarrow \] \[{{(\sqrt{7})}^{2}}={{(3\sqrt{3})}^{2}}+{{4}^{2}}+2(3\sqrt{3})\,(4)\,\cos \theta \] \[\Rightarrow \] \[7=27+16+24\sqrt{3}\,\cos \theta \] \[\Rightarrow \] \[24\sqrt{3}\,\cos \theta =-36\] \[\Rightarrow \] \[\cos \theta =-\frac{3}{2\sqrt{3}}=-\frac{\sqrt{3}}{2}\] \[\Rightarrow \] \[\theta ={{150}^{o}}\]
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