A) \[14\hat{i}-38\hat{j}+16\hat{k}\]
B) \[4\hat{i}+4\hat{j}+6\hat{k}\]
C) \[21\hat{i}+4\hat{j}+4\hat{k}\]
D) \[-14\hat{i}+34\hat{j}-16\hat{k}\]
Correct Answer: A
Solution :
[a] \[\vec{\tau }=\vec{r}\times \vec{F}=(7\hat{i}+3\hat{j}+\hat{k})(-3\hat{i}+\hat{j}+5\hat{k})\] \[\vec{\tau }=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 7 & 3 & 1 \\ -3 & 1 & 5 \\ \end{matrix} \right|=14\hat{i}-38\hat{j}+16\hat{k}\]
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