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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Three Dimensional Geometry

  • question_answer
    The direction consines of two lines are related by\[l+m+n=0\]\[a{{l}^{2}}+b{{m}^{2}}+c{{n}^{2}}=0\]. The lines are parallel if

    A) \[a+b+c=0\]

    B) \[{{a}^{-1}}+{{b}^{-1}}+{{c}^{-1}}=0\]

    C) \[a=b=c\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] For \[n=-(l+m)\], the second relation gives \[a{{l}^{2}}+b{{m}^{2}}+c{{(l+m)}^{2}}=0\] or \[(a+c){{l}^{2}}+2clm+(b+c){{m}^{2}}=0.\] For parallel lines, the two roots must be equal \[\Rightarrow 4{{c}^{2}}-4(b+c)(a+c)=0\Rightarrow ab+bc+ca=0\]


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