Question

What is the torque of the force $\overrightarrow{F}=(2\hat{i}-3\hat{j}+4\hat{k})N$, acting at the point $\overrightarrow{r}=(3\hat{i}+2\hat{j}+3\hat{k})m$ about the origin (in $N-m$):

• A. $6\hat{i}-6\hat{j}+12\hat{k}$
• B. $17\hat{i}-6\hat{j}-13\hat{k}$
• C. $-6\hat{i}+6\hat{j}-12\hat{k}$
• D. $-17\hat{i}+6\hat{j}-13\hat{k}$

Answer 1

The correct option is B $17\hat{i}-6\hat{j}-13\hat{k}$

Torque = $\overline{r}\times \overline{F}$

Where $\overline{r}$ is the arm vector from axis of rotation to the point of application of force.

$\therefore \overline{r}=(3-0)\hat{i}+(2-0)\hat{j}+(3-0)\hat{k}$= $3\hat{i}+2\hat{j}+3\hat{k}$,

$\Rightarrow$ Torque= ($3\hat{i}+2\hat{j}+3\hat{k}$)$\times$($2\hat{i}-3\hat{j}+4\hat{k}$)=$17\hat{i}-6\hat{j}-13\hat{k}$