A) \[14\hat{i}-38\,\hat{J}+16\,\hat{k}\]
B) \[4\hat{i}+4\,\hat{J}+6\,\hat{k}\]
C) \[-14\hat{i}+38\,\hat{J}-16\,\hat{k}\]
D) \[-21\,\hat{i}+3\,\hat{J}+5\,\hat{k}\]
Correct Answer: A
Solution :
Key Idea; Torque can be thought of as rotational force. Torque is defined as the cross product of force vector F and r, distance from the axis of rotation to the point on which the force is acting. \[\therefore \] \[\vec{\tau }=\vec{r}\times \vec{F}\] Given, \[\vec{r}=7\,\hat{i}+3\vec{j}+\vec{k},\,\,\vec{F}=-3\,\hat{i}+\hat{j}+5\hat{k}\] \[\therefore \] \[\vec{\tau }=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 7 & 3 & 1 \\ -3 & 1 & 5 \\ \end{matrix} \right|\] \[=\hat{i}\,\,(15-1)-\hat{j}\,\,(35+3)+\hat{k}\,(7+9)\] \[=14\,\hat{i}-38\,\hat{j}+16\,\hat{k}\]
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