If a and b are unit vectors, then the angle between a and b for which a- 2 b is a unit vector is

Step-by-step solution

Given that a and b are unit vectors, we have | a | = 1 and | b | = 1 . The vector a - 2 b is a unit vector, which implies | a - 2 b | = 1 . Squaring both sides, we get | a - 2 b |^2 = 1^2 . Using the property | u - v |^2 = | u |^2 + | v |^2 - 2( u v ) , we have | a |^2 + | 2 b |^2 - 2( a 2 b ) = 1 . Substituting the magnitudes, 1^2 + 2| b |^2 - 2 2 ( a b ) = 1 . Since | b | = 1 , this simplifies to 1 + 2 - 2 2 ( a b ) = 1 . 3 - 2 2 ( a b ) = 1 . 2 2 ( a b ) = 2 . a b = 2 2 2 = 1 2 . Since a b = | a || b | , we have