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Torque of a Force \(\vec{F}\) acting on a point with position vector \(\vec{r}\) is given by:

\(\vec{\tau}=\vec{r} \times \vec{F}\)

To, we can find Torque by finding the cross product of \(\vec{r}\) and \(\vec{F}\)

We have:

\(\vec{r}=3 \hat{\imath}+2 \hat{\jmath}+3 \hat{k} m\)

\(\vec{F}=2 \hat{\imath}-3 \hat{\jmath}+4 \hat{k} N\)

So, torque will be:

\(\vec{\tau}=\left|\begin{array}{ccc}{\hat{\imath}} & {\hat{\jmath}} & {\hat{k}} \\ {3} & {2} & {3} \\ {2} & {-3} & {4}\end{array}\right|\)

\(\Longrightarrow \vec{\tau}=\hat{\imath}((2)(4)-(-3)(3))-\hat{\jmath}((3)(4)-(2)(3))+\hat{k}((3)(-3)-(2)(2))\)

\(\Longrightarrow \vec{\tau}=\hat{\imath}(8+9)-\hat{\jmath}(12-6)+\hat{k}(-9-4)\)

\(\Longrightarrow[\vec{\tau}=17 \hat{\imath}-6 \hat{\jmath}-13 \hat{k}, N m]\)

This is the torque of the force acting about Origin.