A) \[\mathbf{i}+2\mathbf{j}-4\mathbf{k}\]
B) \[\mathbf{i}-2\mathbf{j}-4\mathbf{k}\]
C) \[\mathbf{i}+2\mathbf{j}+4\mathbf{k}\]
D) \[\mathbf{i}-2\mathbf{j}+4\mathbf{k}\]
Correct Answer: C
Solution :
Force \[(\overrightarrow{F})=2\mathbf{i}+\mathbf{j}-\mathbf{k}\] and its position vector \[=2\,\mathbf{i}-\mathbf{j}\]. We know that the position vector of a force about origin \[(\mathbf{r})=(2\mathbf{i}-\mathbf{j})-(0\mathbf{i}+0\mathbf{j}+0\mathbf{k})\] or \[\mathbf{r}=2\,\mathbf{i}-\mathbf{j}\]. Therefore, moment of the force about origin \[=\mathbf{r}\times \overrightarrow{F}=\left| \begin{align} & \,\mathbf{i}\,\,\,\,\,\,\mathbf{j}\,\,\,\,\,\,\,\mathbf{k} \\ & \,2\,\,-1\,\,\,\,\,0 \\ & \,2\,\,\,\,\,1\,\,\,\,-\,1 \\ \end{align} \right|=\mathbf{i}+2\mathbf{j}+4\mathbf{k}\].
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