Question

The torque of force $\overrightarrow{F}=2\hat{i}-3\hat{j}+4\hat{k}$ newton acting at a point $\overrightarrow{r}=3\hat{i}+2\hat{j}+3\hat{k}$ metre about is:-

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

Answer 1

The correct option is D $-17\hat{i}+6\hat{j}+13\hat{k}N-m$

We know torque$\tau =\overrightarrow{F}\times \overrightarrow{r}$

$\tau =|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& -3& 4\\ 3& 2& 3\end{array}|$

$\hat{i}(-9-8)-\hat{j}(6-12)+\hat{k}(4+9)=-17\hat{i}+6\hat{j}+13\hat{k}$