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

Given a ( b c ) = b + c 2 , expand the triple product using the identity a ( b c ) = ( a c ) b - ( a b ) c . This yields ( a c ) b - ( a b ) c = 1 2 b + 1 2 c . Since a , b , and c are non-coplanar unit vectors and thus linearly independent, equate coefficients: a c = 1 2 -( a b ) = 1 2 Solving gives a b = - 1 2 . For unit vectors, the dot product equals , where is the angle between a and b . Thus, = - 1 2 , so = 3 4 . The angle between a and b is 3 4 .