The resultant of two vectors A and B is perpendicular to A and the magnitude is 1 2 times that of B . The angle between A and B is

Step-by-step solution

Let the angle between A and B be . The resultant vector is R = A + B . Since R is perpendicular to A , their dot product is zero: R A = 0 ( A + B ) A = 0 A^2 + AB = 0 = - A B The magnitude of the resultant is given by: R^2 = A^2 + B^2 + 2AB Substituting = - A B into the equation: R^2 = A^2 + B^2 + 2AB (- A B ) R^2 = B^2 - A^2 It is given that R = B 2 , so R^2 = B^2 2 . B^2 2 = B^2 - A^2 A^2 = B^2 2 A = B 2 Substituting the value of A in the expression for : = - B 2 B = - 1 2 = 135^ Answer: 135^