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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2009

  • question_answer
    Let a plane passes through the point P(-1, -1,1) and also passes through a line joining the points Q (0,1,1) and R(Q,0,2). Then, the distance of plane from the point (0,0,0) is

    A)  3                

    B)  0

    C)  \[1/\sqrt{6}\]             

    D)  \[2/\sqrt{6}\]

    Correct Answer: D

    Solution :

     Let the equation of plane passing through the point P (-1, -1,1) is \[a(x+1)+b(y+1)+c(z-1)=0\] ?.(i) which passes through the points Q (0,1,1) and R (0,0,2). \[\therefore \] \[a+2b+0c=0\] and            \[a+b+c=0\] \[\Rightarrow \] \[\frac{a}{2-0}=-\frac{b}{1-0}=\frac{c}{1-2}\] \[\Rightarrow \] \[\frac{a}{2}=\frac{b}{-1}=\frac{c}{-1}\] From Eq. (i), \[2(x+1)-y(y+1)-1(z-1)=0\] \[\Rightarrow \] \[2x-y-z+2=0\] \[\therefore \]Distance of plane from point (0, 0, 0) \[=\frac{0+0+0+2}{\sqrt{{{2}^{2}}+{{(-1)}^{2}}+{{(-1)}^{2}}}}=\frac{2}{\sqrt{6}}\]


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