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JEE Main & Advanced Mathematics Vector Algebra Question Bank Scalar triple product and their applications

  • question_answer
    If vectors \[\vec{A}=2\mathbf{i}+3\mathbf{j}+4\mathbf{k}\], \[\vec{B}=\mathbf{i}+\mathbf{j}+5\mathbf{k}\], and \[\vec{C}\] form a left handed system, then \[\vec{C}\] is                      [Roorkee 1999]

    A)             11i ? 6j ? k

    B)             ? 11i + 6j + k

    C)             11i ? 6j + k

    D)             ? 11i + 6j ? k

    Correct Answer: B

    Solution :

                    \[\overrightarrow{A}=2i+3j+4k\] and \[\overrightarrow{B}=i+j+5k\]                 \[\overrightarrow{A},\,\overrightarrow{B}\] and \[\overrightarrow{C}\] form a left or right handed system according as \[[\overrightarrow{A}\,\overrightarrow{B}\,\overrightarrow{C}]<0\] or \[>0\] respectively.                                 Here, \[[\overrightarrow{A}\,\overrightarrow{B}\,\overrightarrow{C}]<0\],  \ \[\overrightarrow{C}=-11i+6j+k.\]


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