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

Step-by-step solution

Given a ( b c ) = b 2 Using the vector triple product expansion, we have: ( a c ) b - ( a b ) c = 1 2 b Rearranging the terms, we get: ( a c - 1 2 ) b - ( a b ) c = 0 Since a , b , c are non-coplanar vectors, b and c must be non-collinear. Therefore, their coefficients must be independently zero: a c - 1 2 = 0 a c = 1 2 a b = 0 Since a and b are non-zero vectors, a b = 0 implies that a is perpendicular to b . Thus, the angle between a and b is 2 . Answer: 2