Physics

Problem

Two equal and opposite forces

\vec{F}

and

-\vec{F}

act respectively at points with position vectors

\vec{r}_1=(4,2,-1)\,\text{m}

and

\vec{r}_2=(1,5,3)\,\text{m}

. The forces are perpendicular to the vector joining the two points, and the resulting couple has moment

\vec{\tau}=4\mathbf{i}-4\mathbf{j}+6\mathbf{k}\,\text{N m}

. Determine the vector

\vec{F}