JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    The equation of the plane passing through the line of intersection of the planes \[x+y+z=1\] and \[2x+3y-z+4=0\]and parallel to x-axis is

    A)            \[y-3z-6=0\]

    B)            \[y-3z+6=0\]

    C)            \[y-z-1=0\]

    D)            \[y-z+1=0\]

    Correct Answer: B

    Solution :

               Equation of plane passing through intersection of given planes is, \[(x+y+z-1)+\lambda \,(2x+3y-z+4)=0\] ?..(i)            Plane (i) is parallel to x-axis, then \[\,(1+2\lambda )\,1=0\,\]                    Þ \[\lambda =-\frac{1}{2}\]                    Put the value of \[\lambda \] in (i), we get \[y-3z+6=0\], which is the required plane.

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