If a , b , c are three vectors such that | a + b + c |=1 , c = ( a b ) and | a |= 1 3 ,| b |= 1 2 ,| c |= 1 6 , then the angle between a and b is

Step-by-step solution

Let be the angle between a and b . aligned & Since c = ( a b ) & c a , c b & c a = c b =0 aligned Now, aligned & | a + b + c |=1 & | a + b + c |^2=1 & | a |^2+| b |^2+| c |^2+2( a b + b c + c a )=1 & 1 3 + 1 2 + 1 6 +2 | a || b | =1 & =0 & = 2 aligned