The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters.

Question

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec{F}=\hat{i}-\hat{j}+\hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in $z$-direction is $\_\_\_\_$ .\

Professor PC Thomas Classes · Answer

(2) : As, $\vec{	au}=\vec{r} 	imes \vec{F}$ and $$ \begin{aligned} & \vec{F}=\hat{i}-\hat{j}+\hat{k}, \vec{r}=\hat{i}+\hat{j}+\hat{k} ; \vec{	au}=\left[\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \ 1 & 1 & 1 \ 1 & -1 & 1 \end{array}ight] \ & \vec{	au}=\hat{i}(1-(-1)-\hat{j}(1-1)+\hat{k}(-1-1) \ & \vec{	au}=2 \hat{i}-2 \hat{k} \end{aligned} $$ Here, $	au_{x}=2, 	au_{z}=2$\