A) \[\frac{150}{11}\,(2\mathbf{i}-3\mathbf{j})\]
B) \[\frac{6}{11}\,(50\mathbf{i}-75\mathbf{j}+36\mathbf{k})\]
C) \[150\,(2\mathbf{i}-3\mathbf{j})\]
D) \[6\,(50\mathbf{i}-75\mathbf{j}+36\mathbf{k})\]
Correct Answer: A
Solution :
\[\overrightarrow{OA}=3\mathbf{i}+2\mathbf{j}-9\mathbf{k};\] \[\mathbf{F}=(9\mathbf{i}+6\mathbf{j}-2\mathbf{k})\times \frac{6}{11}\] \[\therefore \] Moment \[=\overrightarrow{OA}\times \mathbf{F}=\frac{6}{11}\left| \,\begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 3 & 2 & -9 \\ 9 & 6 & -2 \\ \end{matrix}\, \right|\] \[=\frac{6}{11}(50\mathbf{i}-75\mathbf{j})=\frac{150}{11}(2\mathbf{i}-3\mathbf{j})\].
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