A) \[41\hat{i}-8\hat{j}+55\hat{k}\]
B) \[-408\hat{i}-12\hat{j}+135\hat{k}\]
C) \[-36\hat{i}+14\hat{j}-35\hat{k}\]
D) None of the above
Correct Answer: B
Solution :
Let\[\overrightarrow{F}=5\hat{i}+10\hat{j}+16\hat{k}\] Here, \[\overrightarrow{r}=2\hat{i}-7\hat{j}+10\hat{k}-(-5\hat{i}+6\hat{j}-10\hat{k})\] \[=7\hat{i}-13\hat{j}+20\hat{k}\] \[\therefore \] Moment \[=\overrightarrow{r}\times \overrightarrow{F}\] \[=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 7 & -13 & 20 \\ 5 & 10 & 16 \\ \end{matrix} \right|\] \[=\hat{i}(208-200)-\hat{j}(112-100)+\hat{k}(70+65)\] \[=-408\hat{i}-12\hat{j}+135\hat{k}\]
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