One force acting on a machine part is F = (-5.00 N)i + (4.00 N)j. The vector from the origin to the point where the force is applied is r = (-0.450 m)i +(0.150 m)j. In a sketch, show r, F, and the origin.

Calculate the torque (magnitude and direction) about point O due to the force F in each of the cases sketched in Fig. E10.1. In each case, both the force F and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude F = 10.0 N.

A metal bar is in the $xy$-plane with one end of the bar at the origin. A force $\(\overrightarrow{F}\)=\(\left\)(7.00N\(\right\))i+(-3.00N)j$ is applied to the bar at the point $x=3.00\(\text{ m}\)$, $y=4.00\(\text{ m}\)$. What are the magnitude and direction of the torque with respect to the origin produced by $\overrightarrow{F}$?

A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0-N force at the end of the handle at 37° with the handle (Fig. E10.7). What torque does the machinist exert about the center of the nut?

A metal bar is in the $xy$-plane with one end of the bar at the origin. A force $\overrightarrow{F}=\left(7.00N\right)i+(-3.00N)j$ is applied to the bar at the point $x=3.00\text{ m}$, $y=4.00\text{ m}$. In terms of unit vectors $i$ and $j$, what is the position vector $r$ for the point where the force is applied?