A force of - P k ^ acts on the origin of the coordinate system. The torque about the point ( 2 , - 3 ) is P…

It is given that the force $\overrightarrow{F}=-P\hat{k}$

The coordinates of the origin is $(0,0)$.

The coordinates of the point given is  $(2,-3)$

The displacement vector is 

$\overrightarrow{r}=(0-2)\hat{i}+(0+3)\hat{j}=-2\hat{i}+3\hat{j}$

Hence, the torque is 

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=(-2\hat{i}+3\hat{j})\times (-P\hat{k})$

$\Rightarrow \overrightarrow{\tau }=-2P\hat{j}-3P\hat{i}=P(a\hat{i}+b\hat{j})$

So, it can be written

$\mathrm{a}=-3$, $b=-2$

$\therefore \frac{a}{b}=\left(\frac{3}{2}\right)\Rightarrow$ so $x=3$