p and q are two components of a given force f and its line of action divides the angle between them in the ratio of 1:2 ,prove that q(f+q)=p^2

Answer 1

1. Answer: It doesn't work, someone feel free to correct
2. Method:
3. components will always form a 90 degree angle (for example x and y components are 90 degrees from each other). If its a 1:2 ratio, then p must be 30 degrees and q is 60 degrees. Assuming p is up (mimicking the yaxis) and q is to the right (mimicking the xaxis), the components would be: p = fsin(60), q = fcos(60)
4. q(f + q) = p^2

fcos(60) ( f + fsin(60)) = f^2 * sin(60)^2

f^2*cos(60) + f^2 * cos(60)sin(60) = f^2 * sin(60)^2

1 + sin(60) = sin(60) * tan(60)

1.9 = 1.5

The right side is not equal to the left