The sum of the magnitudes of two vectors acting at a point is 18 and the magnitude of their resultant is 12 . If the resultant is at 90^ with the vector of smaller magnitude, then the magnitudes of the vectors are

Step-by-step solution

Let two vector be A and B aligned & | A |+| B |=18 & | R |=12 aligned Let | A | be x , then | B |=18- x aligned & | R |= | A |^2-| B |^2 & 12= x^2-(18-x)^2 & 144=x^2- (324+x^2-36 x ) & 144=x^2-324-x^2+36 x aligned aligned & 36 x=468 | A |=x=13 & | B |=18-x=18-13=5 aligned