Question

two forces F1 and F2 acting on a body have a resultant R1 if F2 is double that new resultant is R2 forms are right angle with F1 prove that are r1 and F2 have the same magnitude

Answer 1

let a be the angle between f1 and f2. f1+f2=r1______(1) f1+2f2=r2_____(2) r1*r1=f1*f1+f1*f2+f2*f1*f2+f2. =r12=f1^2+f2^2+2f1*f2*a______(3) f1*(f1+2f2)=f1*r2. since f1 and r2 are perpendicular f1*r2=0. f1^2+2f1*a=0. by,equation (3) and (4) r1^2=f1^2+2f1*f2a+f2^2. r1^2=0+f2^2. r1=f2