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JEE Main & Advanced Mathematics Vector Algebra Question Bank Vector or Cross product of two vectors and its application

  • question_answer
    Let the points A, B and P be (? 2, 2, 4), (2, 6, 3) and (1,2,1) respectively. The magnitude of the moment of the force represented by \[\overrightarrow{AB}\] and acting at A about P is [MP PET 1987]

    A)                 15

    B)                 \[3\sqrt{41}\]

    C)                 \[3\sqrt{57}\]

    D)                 None of these

    Correct Answer: B

    Solution :

               \[\mathbf{F}=\overrightarrow{AB}=4\mathbf{i}+4\mathbf{j}-\mathbf{k}\] and \[\overrightarrow{AP}=3\mathbf{i}-3\mathbf{k}\]            Moment of the force is \[\overrightarrow{AP}\times \overrightarrow{AB}\]            \[=\left| \begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    3 & 0 & -3  \\    4 & 4 & -1  \\ \end{matrix} \right|=12\mathbf{i}-9\mathbf{j}+12\mathbf{k}\]                 \[\therefore \] Magnitude is, \[\sqrt{144+81+144}=3\sqrt{41}.\]


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