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