JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    If the plane \[x-3y+5z=d\]passes through the point (1,2,4), then the lengths of intercepts cut by it on the axes of x, y, z are respectively [MP PET 1998]

    A)            15, ?5, 3

    B)            1, ?5, 3

    C)            ?15, 5, ?3

    D)            1, ?6, 20

    Correct Answer: A

    Solution :

               If plane \[x-3y+5z=d\] passes through point (1, 2, 4). Then \[1-6+20=d\,\,\Rightarrow \,\,d=15\]            \[\therefore \,\,\]Plane, \[x-3y+5z=15\]\[\Rightarrow \,\,\frac{x}{15}+\frac{y}{-5}+\frac{z}{3}=1\]            Hence length of intercept cut by it on the axes (x, y, z) are respectively (15, ? 5, 3).


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