A) \[3/2\]
B) \[-3/2\]
C) \[2/3\]
D) \[-2/3\]
Correct Answer: B
Solution :
Unit vectors \[\vec{a},\vec{b},\vec{c}\]and \[\vec{a}+\vec{b}+\vec{c}=0\]\[\vec{a},\vec{b},\vec{c}\]are unit vector, therefore \[|\vec{a}|=|\vec{b}|=|\vec{c}|=1\]and \[{{(\vec{a}+\vec{b}+\vec{c})}^{2}}=0\]or \[|\vec{a}{{|}^{2}}+|\vec{b}{{|}^{2}}+|\vec{c}{{|}^{2}}+2\vec{a}\vec{b}\] \[+\,2\vec{b}.\vec{c}+2\vec{c}\,\vec{a}=0\] or \[2(\vec{a}.\vec{b}.\vec{c}+\vec{c}.\vec{a})=-3\] therefore \[\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}=-3/2\]
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