Question

A force $F=Ai+Bj$ is applied to a point whose radius vector relative to the origin of coordinates $O$ is equal to $r=ai+bj$, where $a,b,A,B$ are constants, and $i,j$ are the unit vector of the $x$ and $y$ axes $a,b,A,B$ are constants, Find the arm $l$ of the force $F$ relative to the point $O$.

Answer 1

Sought moment $\overrightarrow{N}=\overrightarrow{r}\times \overrightarrow{F}=(a\overrightarrow{i}+b\overrightarrow{j})\times (A\overrightarrow{i}+B\overrightarrow{j})$

$=aB\overrightarrow{k}+Ab(-\overrightarrow{k})=(aB-Ab)\overrightarrow{k}$

an arm of the force $l=\frac{N}{F}=\frac{aB-Ab}{\sqrt{A^2+B^2}}$