If a,b,c are unit vectors such that `a+b+c=0`, then find the value of `a.b+b.c+c.a`.

Explanation

Given , `|a|=|b|=|c|=1 and a +b+c=0`
We have `(ab+c).(a+b+c)=0`
`rArr a.(a+b+c)+b.(a+b+c)+c.(a+b+c)=0`
`rArr a.a+a.b+a.c+b.a+b.b+b.c+c.a+c.b+c.c=0`
`rArr |a|^2+|b|^2+|c|^2+2(a.b+b.c+c.a)=0`
`(because a.a =|a|^2 and a.b=b.a)`
`rArr 1+1+1+2(a.b+b.c+c.a)=0`
`(because |a|=|b|=|c|=1)`
`rArr 3+2(a.b+b.c+c.a)=0`
`rArr a.b+b.c+c.a=-(3)/(2)`.