If a , b and c are unit vectors such that a + b + c = 0 , then angle between a and b is

Step-by-step solution

Given, a , b , c are unit vectors. array lc & |a|=|b|=|c|=1 Also, given & a + b + c =0 & (a+b)=-c array Squaring on both sides, we get array lc & ( a + b )²=( c )² & ( a )²+( b )²+2 a b =( c )² & | a |²+| c |²+2 a b =| c |² & [ ( a )²=| a |² ] & 1+1+2 a b =1[ from Eq. (i) ] & 2 b =-1 & a b =-1 / 2=| a || b | & 0=-1 / 2= 2 / 3 [ from Eq. (i) ] & =2 / 3 array