If a , b , c are non-coplanar unit vectors such that a ( b c )= b c 2 , then the angle between a and b is

Step-by-step solution

a ( b c )= b + c 2 aligned & ( a c ) b -( a b ) c = b + c 2 & ( a c - 1 2 ) b - ( a b + 1 2 ) c =0 aligned Since a , b , c are non-coplanar unit vectors, aligned & a b + 1 2 =0 & a b =- 1 2 & | a || b | =- 1 2 & =- 1 2 & = 3 4 aligned [Note: In the question, b c 2 is changed to b + c 2 to apply appropriate textual concepts.]