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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 \[\mathbf{a}\ne \mathbf{0},\,\,\mathbf{b}\ne \mathbf{0}\] and \[|\mathbf{a}+\mathbf{b}|\,=\,|\mathbf{a}-\mathbf{b}|,\] then the vectors a and b are [Roorkee 1986; MNR 1988; IIT Screening 1989; MP PET 1990, 97; RPET 1984, 90, 96, 99; KCET 1999]

    A)             Parallel to each other

    B)             Perpendicular to each other

    C)             Inclined at an angle of \[{{60}^{o}}\]

    D)             Neither perpendicular nor parallel

    Correct Answer: B

    Solution :

               \[|\mathbf{a}+\mathbf{b}|=|\mathbf{a}-\mathbf{b}|\]; Squaring both sides, we get \[4\mathbf{a}.\mathbf{b}=0\]                 \[\Rightarrow \mathbf{a}\] is perpendicular to \[\mathbf{b}.\]


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