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J & K CET Engineering J and K - CET Engineering Solved Paper-2005

  • 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

    A)  \[3x-4y+18z+32=0\]

    B)  \[3x+4y-18x+32=0\]

    C)  \[4x+3y-17z+31=0\]

    D)  \[4x-3y+z+1=0\]

    Correct Answer: D

    Solution :

    Any plane passing through \[(0,1,2)\] is \[a(x-0)+b(y-1)+c(z-2)=0\] \[\Rightarrow \] \[ax+b(y-1)+x(z-2)=0\] ?(i) Since, it is passing through \[(-1,0,3),\] we get \[-a-b+c=0\] ?.(ii) Also, Eq. (i) is perpendicular to \[2x+3y+z=5\] \[2a+3b+c=0\] ?.(iii) On solving Eqs. (ii) and (iii), we get \[a=-4,\,\,b=3,\,\,c=-1\] Substituting the values of a, b and c in Eq. (i), we get \[-4x+3(y-1)-1(z-2)=0\] \[\Rightarrow \] \[-4x+3y-3-z+2=0\] \[\Rightarrow \] \[-4x+3y-z-1=0\] \[\Rightarrow \] \[4x-3y+z+1=0\]


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