if vector a,vector b,vector c,are unit vectorssuch that their sum is equal to 0,find the value of a.b vector+b.c vector+c.a vector

Here bold stands for vector and lets mag.a=a=1, mag.b=b=1, mag.c=c=1

Since all these are unit vectors and since their sum is zero, we have

(a+b+c).(a+b+c)=0.0=0

Now expanding the left hand side term by term we get

a²+ b²+ c²+2(ab+bc+ca)=0

or, ab+bc+ca=-3/2