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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line and Plane

  • question_answer
    The ratio in which the line joining the points  (a, b, c) and   (?a, ?c, ?b) is divided by the xy-plane is [MP PET 1994]

    A)            \[a:b\]

    B)            \[b:c\]

    C)            \[c:a\]

    D)            \[c:b\]

    Correct Answer: D

    Solution :

                       Let the ratio be k : 1. Since on xy-plane z = 0            \[\Rightarrow \,\,\frac{-bk+c}{k+1}=0\,\,\Rightarrow \,\,k=\frac{c}{b}\].  Hence the ratio is c : b.                    Aliter : Using formula, required ratio is \[-\frac{c}{-b}=c\,\,:\,\,b.\]


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