If three unit vectors a , b , c satisfy a + b + c = 0 , then the angle between a and b is

Step-by-step solution

Given, condition is a + b + c = 0 ...(i) and a , b , c are the unit vectors. Then | a |=| b |=| c |=1 Let the angle between a and b is . Now, from Eq. (i) a + b + c =0( a + b )=- c Squaring on both sides ( a + b )^2=( c )^2 [ ( c )^2=| c |^2 ] ( a )^2+( b )^2+2( a ) ( b )=| c |^2 | a |^2+| b |^2+2 a b =| c |^2 1+1+2 | a || b | =1[ a b =| a || b | ] 2 1 1 =-1 = -1 2 = ( 2 3 ) = 2 3