Problem 1.236

A force \(\mathbf{F}_ {1}=A \mathbf{j}\) is applied to a point whose radius vector \(r_{1}=a i\), while a force \(F_{2}=B i\) is applied to the point whose radius vector \(\mathbf{r}_ {2}=b \mathbf{j} .\) Both radius vectors are determined relative to the origin of coordinates \(O, \mathbf{i}\) and \(\mathbf{j}\) 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 \(O\).