Question

The torque of the force $\overrightarrow{F}=\left(2\hat{i}-3\hat{j}+4\hat{k}\right)N$ acting at a point $\overrightarrow{r}=\left(3\hat{i}+2\hat{j}+3\hat{k}\right)m$ about the origin will 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 $17\hat{i}-6\hat{j}-13\hat{k}$

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