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

  • question_answer
    The position vector of vertices of a triangle ABC are \[4\mathbf{i}-2\mathbf{j},\,\mathbf{i}+4\mathbf{j}-3\mathbf{k}\] and \[-\mathbf{i}+5\mathbf{j}+\mathbf{k}\] respectively, then \[\angle ABC=\] [RPET 1988, 97]

    A)             \[\pi /6\]

    B)             \[\pi /4\]

    C)             \[\pi /3\]

    D)             \[\pi /2\]

    Correct Answer: D

    Solution :

                    Here \[\overrightarrow{AB}=-3\mathbf{i}+6\mathbf{j}-3\mathbf{k},\] \[\overrightarrow{BC}=-2\mathbf{i}+\mathbf{j}+4\mathbf{k}\] and \[\overrightarrow{AB}\,.\,\overrightarrow{BC}=6+6-12=0\Rightarrow \angle ABC=90{}^\circ .\]


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