Vector Cross Product/Examples/Couple Exerted by Force

Example of Vector Cross Product
Let $\mathbf F$ be a force acting at a point $P$ on a body $B$ axially about an axis of rotation $R$ such that the distance from $P$ to $R$ is represented by the displacement vector $\mathbf d$.

Then the couple exerted on $B$ by $\mathbf F$ is defined as:
 * $\mathbf T = \mathbf F \times \mathbf d = \norm {\mathbf F} \norm {\mathbf d} \mathbf {\hat t} \sin \theta$

where:
 * $\times$ denotes vector cross product
 * $\mathbf {\hat t}$ denotes the unit vector perpendicular to both $\mathbf F$ and $\mathbf d$ according to the right-hand screw rule
 * $\theta$ is the angle between the directions of $\mathbf F$ and $\mathbf d$.