Question

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 be

• 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$\hat{k}$

$\overrightarrow{\tau }$ = $\overrightarrow{\tau }$ $\times$ $\overrightarrow{F}$= $\lceil \begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 2& 3\\ 2& -3& 4\end{array}\rceil$
= [(2 $\times$ 4)-(3 $\times$ -3)]$\hat{i}$ + (2 $\times$ 3)-(3 $\times$ 4)]$\hat{j}$ + (3 $\times$ -3)-(2 $\times$ 2)]$\hat{k}$
= 17$\hat{i}$ - 6$\hat{j}$ - 13$\hat{k}$