A) \[\hat{i}-5\hat{j}+8\hat{k}\]
B) \[2\hat{i}+2\hat{j}+2\hat{k}\]
C) \[\hat{i}+\hat{j}+\hat{k}\]
D) \[3\hat{i}+2\hat{j}+3\hat{k}\]
Correct Answer: A
Solution :
Torque \[(\tau )=r\times F\] \[=(2\hat{i}+2\hat{j}+\hat{k})\times (3\hat{i}+7\hat{j}+4\hat{k})\] \[=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 2 & 2 & 1 \\ 3 & 7 & 4 \\ \end{matrix} \right|\] \[=\hat{i}(8-7)-\hat{j}(8-3)+\hat{k}(14-6)\] \[=\hat{i}-5\hat{j}+8\hat{k}\]
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