Q.A force $\vec F = (3\hat i + 4\hat j)\ \text{N}$ acts at a point whose position vector, measured from the origin $O$, is $\vec r = (2\hat i + 1\hat j)\ \text{m}$. Find the torque of this force about $O$.

Torque (or moment of a force) is the rotational analogue of force, defined as $\vec{\tau}=\vec{r}\times\vec{F}$, where $\vec{F}$ is the applied force and $\vec{r}$ is the position vector of its point of application measured from the axis of rotation; its magnitude is $\tau=rF\sin\theta$, where theta is the angle between $\vec{r}$ and $\vec{F}$. A force's rotational effectiveness depends on three things: the force's magnitude, how far from the axis it is applied (larger r gives larger torque), and the angle at which it is applied (maximum effect at 90 degrees, zero effect when applied along the line to the axis). …