Question

Magnitude of torque of force $\overrightarrow{F}=2\hat{i}-3\hat{j}+\hat{k}$ acting at a point (3,2,-1) about a point having coordinate (1,-2,3) is

• A. 18 N-m
• B. $8\sqrt{5}$ N-m
• C. 20 N-m
• D. $6\sqrt{10}$ N-m

Answer 1

The correct option is D $6\sqrt{10}$ N-m

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}\text{where}\overrightarrow{r}=(3\hat{i}+2\hat{j}-\hat{k})-(\hat{i}-2\hat{j}+3\hat{k})$

$\overrightarrow{r}=2\hat{i}+4\hat{j}-4\hat{k})$ &
so $\overrightarrow{\tau }=(2\hat{i}+4\hat{j}-4\hat{k})\times (2\hat{i}-3\hat{j}+\hat{k})=-8\hat{i}-10\hat{j}-14\hat{k}$