A force F,hat{k} acts at the origin O of a co | vedclass

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(C) The force is given by $\vec{F} = F\,\hat{k}$.The position vector of the origin $O(0, 0, 0)$ with respect to the point $P(1, -1, 0)$ is $\vec{r} =

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

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(C) The force is given by $\vec{F} = F\,\hat{k}$.The position vector of the origin $O(0, 0, 0)$ with respect to the point $P(1, -1, 0)$ is $\vec{r} = (0 - 1)\hat{i} + (0 - (-1))\hat{j} + (0 - 0)\hat{k} = -\hat{i} + \hat{j}$.The torque $\vec{	au}$ is given by $\vec{	au} = \vec{r} 	imes \vec{F}$.$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ -1 & 1 & 0 \ 0 & 0 & F \end{vmatrix}$.Expanding the determinant:$\vec{	au} = \hat{i}(1 \cdot F - 0 \cdot 0) - \hat{j}((-1) \cdot F - 0 \cdot 0) + \hat{k}((-1) \cdot 0 - 1 \cdot 0)$.$\vec{	au} = F\,\hat{i} + F\,\hat{j} = F\,(\hat{i} + \hat{j})$.

$A$ force $F\,\hat{k}$ acts at the origin $O$ of a coordinate system. What is the torque about the point $(1, -1, 0)$?

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