If a and b have the same magnitude and angle between them is 60^ and their scalar product is 1 2 , then | a | is ____

Step-by-step solution

Let | a | = | b | = x . The scalar product of two vectors is given by a b = | a | | b | . Substituting the given values: 1 2 = x^2 60^ 1 2 = x^2 ( 1 2 ) x^2 = 1 Since magnitude cannot be negative, x = 1 . Therefore, | a | = 1 .