A force `F_1=Aj` is applied to a point whose radius vector `r_1=ai`, while a force `F_2=Bi` is applied to the point whose radius vector `r_2=bj`. Both radius vectors are determined relative to the origin of coordinates O, i and j are the unit vectors of the x and y axes, a, b, A, B are constants. Find the arm l of the resultant force relative to the point O.

Explanation

Relative to point O, the net moment of force:
`vecN=vecr_1xxvecF_1+vecr_2xxvecF_2=(avecixxAvecj)+(BvecjxxBveci)`
`=abveck+AB(-veck)=(ab-AB)veck` (1)
Resulatnt of the external force
`vecF=vecF_1+vecF_2=Avecj+Bvecj` (2)
As `vecN*vecF=0` (as `vecN_|_vecF`) so the sought arm `l` of the force `vecF`
`l=N//F=(ab-AB)/(sqrt(A^2+B^2))`