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JEE Main & Advanced Mathematics Vector Algebra Question Bank Critical Thinking

  • question_answer
    The moment about the point \[M(-2,\,4,\,-6)\] of the force represented in magnitude and position by \[\overrightarrow{AB}\] where the points A and B have the co-ordinates \[(1,\,2,\,-3)\] and \[(3,\,-4,\,2)\] respectively, is [MP PET 2000]

    A) 8i - 9j - 14k

    B) 2i - 6j + 5k

    C) - 3i + 2j - 3k

    D) - 5i + 8j - 8k

    Correct Answer: A

    Solution :

    • Force \[\mathbf{F}=\overrightarrow{AB}=\left( 3-1 \right)\,i+\left( -4-2 \right)\,j+\left( 2+3 \right)\,k\]                                  
    • \[=2i-6j+5k\]                   
    • Moment of Force \[\overrightarrow{F}\] w.r.t \[M=\overrightarrow{MA}\times \overrightarrow{F}\]                   
    • \[\because \,\,\,\overrightarrow{MA}=\left( 1+2 \right)\,i+\left( 2-4 \right)\,j+\left( -3+6 \right)\,k\]\[=3i-2j+3k\]                   
    • Now   \[\overrightarrow{MA}\times \overrightarrow{F}=\left| \,\begin{matrix}    i & j & k  \\    3 & -2 & 3  \\    2 & -6 & 5  \\ \end{matrix}\, \right|\]        \[=\mathbf{i}\,\left( -10+18 \right)+\mathbf{j}\,\left( 6-15 \right)+\mathbf{k}\,\left( -18+4 \right)\]\[=8\mathbf{i}-9\mathbf{j}-14\mathbf{k}\].


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