A) \[-21\]
B) \[-\frac{21}{2}\]
C) 21
D) \[\frac{21}{2}\]
E) \[\frac{59}{2}\]
Correct Answer: B
Solution :
\[\because \] \[|\overrightarrow{a}+\overrightarrow{b}|=\sqrt{3}\] \[\Rightarrow \] \[|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}+2\overrightarrow{a}.\overrightarrow{b}=3\] \[\Rightarrow \] \[\overrightarrow{a}.\overrightarrow{b}=\frac{1}{2}\] \[\therefore \] \[(3\overrightarrow{a}-4\overrightarrow{b}).(2\overrightarrow{a}+5\overrightarrow{b})\] \[=6|\overrightarrow{a}{{|}^{2}}+15\overrightarrow{a}.\overrightarrow{b}-8\overrightarrow{a}.\overrightarrow{b}-20|\overrightarrow{b}{{|}^{2}}\] \[=6+7\overrightarrow{a}.\overrightarrow{b}-20\] \[=6+\frac{7}{2}-20=\frac{7-28}{2}=-\frac{21}{2}\]
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