The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle w

Question

The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i}+\hat{j}+\hat{k})$, would be\

Professor PC Thomas Classes · Answer

(c): $\vec{F}=(2 \hat{i}+\hat{j}+2 \hat{k}) \mathrm{N}, \vec{r}=(\hat{i}+\hat{j}+\hat{k}) \mathrm{m}$, $$ \begin{aligned} \vec{	au} & =\vec{r} 	imes \vec{F}=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \ 1 & 1 & 1 \ 2 & 1 & 2 \end{array}ight| \ & =\hat{i}(2-1)-\hat{j}(2-2)+\hat{k}(1-2)=\hat{i}-\hat{k} \end{aligned} $$