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 vectors of the x and y axes. Find the moment N and the arm l of the force F relative to the point O.

Options

A. `(aB-Ab)/(sqrt(A^2+B^2))`
B. `(aA-Bb)/(sqrt(A^2+B^2))`
C. `(aB+Ab)/(sqrt(A^2+B^2))`
D. `(Ab-aB)/(sqrt(A^2+B^2))`

Answer

A

Explanation

Sought moment `vecN=vecrxxvecF=(aveci+bvecj)xx(Aveci+Bvecj)`
`=aBveck+Ab(-veck)=(aB-Ab)veck`
and arm of the force `l=N/F=(aB-Ab)/(sqrt(A^2+B^2))`