A) \[2\sqrt{35}\]
B) \[6\sqrt{10}\]
C) \[4\sqrt{17}\]
D) None of these
Correct Answer: B
Solution :
Let \[{{\mathbf{F}}_{1}}=\mathbf{i}+2\mathbf{j}-3\mathbf{k},\]\[{{\mathbf{F}}_{2}}=2\mathbf{i}+3\mathbf{j}+4\mathbf{k}\], \[{{\mathbf{F}}_{3}}=\mathbf{i}-\mathbf{j}+\mathbf{k}\]. \[O\,(0,\,1,\,2)\] and \[P\,(1,\,-2,\,0)\Rightarrow \overrightarrow{OP}=\mathbf{i}-3\mathbf{j}-2\mathbf{k}\] Resultant force \[(\mathbf{F})={{\mathbf{F}}_{1}}+{{\mathbf{F}}_{2}}+{{\mathbf{F}}_{3}}=4\mathbf{i}+4\mathbf{j}+2\mathbf{k}\] Hence moment of force is \[=\overrightarrow{OP}\times \mathbf{F}\] \[=\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -3 & -2 \\ 4 & 4 & 2 \\ \end{matrix} \right|=2\mathbf{i}-10\mathbf{j}+16\mathbf{k}\] Magnitude of moment of force is \[|\overrightarrow{OP}\times \mathbf{F}|=\sqrt{4+100+256}=6\sqrt{10}.\]
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