A) \[6\hat{i}-6\hat{j}+12\hat{k}\]
B) \[17\hat{i}-6\hat{j}-13\hat{k}\]
C) \[-6\hat{i}+6\hat{j}-12\hat{k}\]
D) \[-17\hat{i}+6\hat{j}+13\hat{k}\]
Correct Answer: B
Solution :
\[\overrightarrow{\tau }=\overrightarrow{r\,}\times \overrightarrow{F}\] \[=\left| \begin{matrix} \hat{i}\,\, & \hat{j}\,\, & {\hat{k}} \\ \,3\,\,\, & \,\,2\,\,\,\,\, & 3 \\ \,2\,\,\, & -3\,\,\,\,\,\, & \,\,4\,\, \\ \end{matrix} \right|\,\] \[=\left[ (2\times 4)-(3\times -3) \right]\,\,\hat{i}+\left[ (2\times 3)-(3\times 4) \right]\,\hat{j}\] \[+\left[ (3\times -3)-(2\times 2) \right]\,\hat{k}\]\[=17\,\hat{i}-6\,\hat{j}-13\,\hat{k}\]
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