A) \[\sqrt{211}\]
B) \[40\]
C) \[\sqrt{54}\]
D) \[2\sqrt{54}\]
E) \[72\]
Correct Answer: B
Solution :
Force \[=-2\hat{i}+6\hat{j}-8\hat{k}\] Let \[P(-2,-1,3)\] and \[\text{O}(1,2,-1)\] Then \[\overrightarrow{r}=\overset{\to }{\mathop{OP}}\,=-3,-3,4\] \[\therefore \] Moment of F about\[O\]is \[\overrightarrow{r}\times \overrightarrow{F}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ -3 & -3 & 4 \\ -2 & 6 & -8 \\ \end{matrix} \right|\] \[=\hat{i}(0)-\hat{j}(32)+\hat{k}(-24)\] \[\therefore \] Magnitude\[=\sqrt{{{32}^{2}}+{{24}^{2}}}\] \[=40\]
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