A) \[14\mathbf{\hat{i}}-38\mathbf{\hat{j}}+16\mathbf{\hat{k}}\]
B) \[4\mathbf{\hat{i}}+4\mathbf{\hat{j}}+6\mathbf{\hat{k}}\]
C) \[-14\mathbf{\hat{i}}+38\mathbf{\hat{j}}-6\mathbf{\hat{k}}\]
D) \[-21\mathbf{\hat{i}}+3\mathbf{\hat{j}}+5\mathbf{\hat{k}}\]
Correct Answer: C
Solution :
Torque \[\tau =\vec{F}\times \vec{r}\] \[=(-3\hat{i}+\hat{j}+5\hat{k})\times (7\hat{i}+3\hat{j}+\hat{k})\] or \[\vec{\tau }=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ -3 & 1 & 5 \\ 7 & 3 & 1 \\ \end{matrix} \right|\] \[=-14\hat{i}+38\hat{j}-16\hat{k}\]
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