question_answer

The torque of a force \[\operatorname{F} =- 3\hat{i} + \hat{j} + 5\hat{k}\] acting at the point \[\operatorname{r}=7\,\widehat{i}+3\,\widehat{j}+\widehat{k}\] is

A)  \[4\,\widehat{i}+4\,\widehat{j}+6\,\hat{k}\]       

B)  \[-21\,\,\widehat{i}+4\,\widehat{j}+4\,\hat{k}\]

C)  \[-14\,\,\widehat{i}+34\,\widehat{j}-16\,\hat{k}\]

D)  \[14\,\,\widehat{i}-38\,\widehat{j}+16\,\hat{k}\]

Correct Answer: D

Solution :

As, force \[\operatorname{F}=-\,3\hat{i}\,\,+\,\,\hat{j}\,\,+\,\,5\hat{k}\] and    \[r=7\hat{i}\,\,+3\,\hat{j}\,\,+\,\,\hat{k}\]