A force `vecF=Ahati+Bhatj` is applied to a point whose radius vector relative to the origin is `vecr=ahati+bhatj`, where `a`, `b`, `A`,`B` are constants and `hati`, `hatj` are unit vectors along the `X` and `Y` axes. Find the torque `vectau` and the arm `l` of the force `vecF` relative to the point `O`.

A force `vecF=Ahati+Bhatj` is applied to a point whose radius vector r

1.	A force `vecF=Ahati+Bhatj` is applied to a point whose radius vector relative to the origin is `vecr=ahati+bhatj`, where `a`, `b`, `A`,`B` are constants and `hati`, `hatj` are unit vectors along the `X` and `Y` axes. Find the torque `vectau` and the arm `l` of the force `vecF` relative to the point `O`.
Answer» `vectau=vecrxxvecF=\|[hati,hatj,hatk],[a,b,0],[A,B,0]\|` `vectau=(aB-bA)hatk` Lever arm `l= (\|vectau\|)/(\|vecF)\|=((aB-bA))/(sqrt(A^(2)+B^(2)))` `{{:(tau=rFsintheta implies r sintheta=(tau)/(F)),(r sin theta:"lever arm"):}}`

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