A) \[-3\]
B) \[-2\]
C) \[-\frac{3}{2}\]
D) \[0\]
Correct Answer: C
Solution :
We have \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\] \[\therefore \,\,|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=0\Rightarrow |\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}{{|}^{2}}=0\] \[\Rightarrow \,\,|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}+|\overrightarrow{c}{{|}^{2}}+2(\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a})=0\] \[\Rightarrow \,1+1+1+2(\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a})=0\] \[\Rightarrow \,\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}=-\frac{3}{2}\]You need to login to perform this action.
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