If a and b are unit vectors such that | a + b |= 3 , then the angle between a and b is

Step-by-step solution

Given that a and b are unit vectors, | a | = | b | = 1 . The magnitude of their sum is provided as | a + b | = 3 . The magnitude squared is expanded as | a + b |^2 = | a |^2 + | b |^2 + 2 a b , leading to ( 3 )^2 = 1^2 + 1^2 + 2 a b . Simplifying, 3 = 2 + 2 a b , so a b = 1 2 . Using the dot product definition, a b = | a || b | = . Thus, = 1 2 , yielding = rccos( 1 2 ) = 3 . Final Answer: B