A force of -F hat{k} acts on O,the origin of | vedclass

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(D) The position vector $\vec{r}$ of the origin $O(0, 0)$ with respect to the point $P(1, -1)$ is given by $\vec{r} = (0 - 1)\hat{i} + (0 - (-1))\hat{

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$-F(\hat{i}+\hat{j})$

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(D) The position vector $\vec{r}$ of the origin $O(0, 0)$ with respect to the point $P(1, -1)$ is given by $\vec{r} = (0 - 1)\hat{i} + (0 - (-1))\hat{j} = -\hat{i} + \hat{j}$.The force acting at the origin is $\vec{F} = -F\hat{k}$.The torque $\vec{	au}$ about the point $P$ is defined as $\vec{	au} = \vec{r} 	imes \vec{F}$.Substituting the values,we get $\vec{	au} = (-\hat{i} + \hat{j}) 	imes (-F\hat{k})$.Using the cross product rules $\hat{i} 	imes \hat{k} = -\hat{j}$ and $\hat{j} 	imes \hat{k} = \hat{i}$,we have:$\vec{	au} = F(\hat{i} 	imes \hat{k}) - F(\hat{j} 	imes \hat{k})$$\vec{	au} = F(-\hat{j}) - F(\hat{i})$$\vec{	au} = -F(\hat{i} + \hat{j})$.

$A$ force of $-F \hat{k}$ acts on $O$,the origin of the coordinate system. The torque about the point $(1, -1)$ is

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