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

  • question_answer
    If \[\overrightarrow{{{F}_{1}}}=\mathbf{i}-\mathbf{j}+\mathbf{k},\] \[\overrightarrow{{{F}_{2}}}=-\mathbf{i}+2\mathbf{j}-\mathbf{k},\] \[\overrightarrow{{{F}_{3}}}=\mathbf{j}-\mathbf{k},\] \[\vec{A}=4\mathbf{i}-3\mathbf{j}-2\mathbf{k}\] and \[\vec{B}=6\mathbf{i}+\mathbf{j}-3\mathbf{k},\] then the scalar product of \[\overrightarrow{{{F}_{1}}}+\overrightarrow{{{F}_{2}}}+\overrightarrow{{{F}_{3}}}\]and \[\overrightarrow{AB}\] will be            [Roorkee 1980]

    A)             3

    B)             6

    C)             9

    D)             12

    Correct Answer: C

    Solution :

                    \[\Sigma \,\mathbf{F}=2\mathbf{j}-\mathbf{k},\] \[\overrightarrow{AB}=2\mathbf{i}+4\mathbf{j}-\mathbf{k}\],  \\[\Sigma \,\mathbf{F}\,.\,\overrightarrow{AB}=8+1=9.\]


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