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

  • question_answer
    The projection of the line \[\frac{x+1}{1}=\frac{y}{2}=\frac{z-1}{3}\]on the plane \[x-2y+z=6\] is the line of intersection of the plane with the plane

    A) \[2x+y+2=0\]

    B) \[3x+y-z=2\]

    C) \[2x-3y+8z=3\]

    D) none of these

    Correct Answer: A

    Solution :

    [a] Equation of the plane through \[\left( -1,\text{ }0,\text{ }1 \right)\] is \[a(x+1)+b(y-0)+c(z-1)=0\]     ...(i) Which id parallel to the given line and perpendicular to the given plane \[-a+2b+3c=0\]             ...(ii) And \[a-2b+c=0\]                      ...(iii) From Eqs. (ii) and (iii), we get             \[c=0,\text{ }a=2b\] From Eq. (i), \[2b(x+1)+by=0\] \[\Rightarrow 2x+y+2=0\]


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