If a and b are unit vectors and is the angle between them, then a + b is a unit vector when is

Step-by-step solution

Given unit vectors a and b , where | a | = 1 and | b | = 1 , and | a + b | = 1 . The magnitude squared expands to | a + b |² = | a |² + 2( a b ) + | b |² . Substituting known values gives 1 = 1 + 2( a b ) + 1 , which simplifies to 2( a b ) = -1 , so a b = - 1 2 . Using the dot product formula a b = | a | | b | = , we find = - 1 2 , yielding = 2 3 . Correct option: B