If a , b and c are unit vectors such that a + b + c = 0 , then the a b + b c + c a is equal to

Step-by-step solution

Given that a , b , c are unit vectors and a + b + c =0 | a |=| b |=| c |=1 Here, a + b + c = 0 Then, ( a + b + c )^2=( 0 )^2 aligned & ( a + b + c ) ( a + b + c )=0 & a a + a b + a c + b a + b b & b c + c a + c b + c c =0 & | a |^2+ a b + c a + a b +| b |^2+ b c & + c a + b c +| c |^2=0 & (1)^2+2 a b +2 b c +2 c a +(1)^2+(1)^2=0 & 2[ a b + b c + c a ]+3=0 & 2[ a b + b c + c a ]=-3 & a b + b c + c a =- 3 2 aligned