The resultant of two vectors A and B is perpendicular to vector A and the resultant magnitude is equal to half of the magnitude of B , then the angle between A and B is

Step-by-step solution

aligned & R = A + B & R= | B | 2 & | B | 2 = A^2+B^2+2 A B & A^2+B^2+2 A B = B^2 4 & A^2+2 A B + 3 B^2 4 =0...(i) & R to A & A ( A + B )=0 & A^2+A B =0 & A B =-A^2...(ii) aligned aligned & put this value in equation (1) & A ^2-2 ~A ^2+ 3 ~B ^2 4 =0 & ~A ^2- 3 ~B ^2 4 =0 A = 3 ~B 2 aligned from equation (2), aligned & =- A B = 3 2 B B & = 150 =150^ aligned