JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    The equation of the plane passing through the points (0, 1, 2) and (?1, 0, 3) and perpendicular to the plane            \[2x+3y+z=5\] is [J & K 2005]

    A)            \[3x-4y+18z+32=0\]

    B)            \[3x+4y-18z+32=0\]

    C)            \[4x+3y-17z+31=0\]

    D)            \[4x-3y+z+1=0\]

    Correct Answer: D

    Solution :

               Equation of any plane passing through  (0, 1, 2) is                                 \[a(x-0)+b(y-1)+c(z-2)=0\]           ......(i)                    Plane (i) passes through (?1, 0, 3), then                                 \[a(-1-0)+b(0-1)+c(3-2)=0\]                    Þ \[-a-b+c=0\]Þ \[a+b-c=0\]                                .....(ii)                    Plane (i) is perpendicular to the plane \[2x+3y+z=5\], then \[2a+3b+c=0\]                                         ......(iii)                    Solving (ii) and (iii), we get \[a=-4k,b=3k,c=-k\]                    Putting these values in (i),                        \[-4k(x)+3k(y-1)-k(z-2)=0\]                    Þ \[-4x+3y-3-z+2=0\]                    Þ \[-4x+3y-z-1=0\] Þ \[4x-3y+z+1=0\].

You need to login to perform this action.
You will be redirected in 3 sec spinner