A) 6
B) \[\frac{\sqrt{3}}{2}\]
C) 12
D) 4
E) 16
Correct Answer: D
Solution :
\[\because \]\[\overrightarrow{a}.\overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}|\cos \frac{5\pi }{6}\] \[=-\frac{|\overrightarrow{a}||\overrightarrow{b}|\sqrt{3}}{2}\] Since, the projection of\[\overrightarrow{a}\]in the direction of\[\overrightarrow{b}\] \[\therefore \] \[-\frac{6}{\sqrt{3}}=-\frac{|\overrightarrow{a}||\overrightarrow{b}|\sqrt{3}}{2|\overrightarrow{b}|}\] \[\Rightarrow \] \[|\overrightarrow{a}|=\frac{6\times 2}{3}=4\]
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