Q73 / 160 · TS EAMCET 2017 · Mathematics

A point on the plane that passes through the points $(1,-1,6),(0,0,7)$ and perpendicular to the plane $x-2 y+z=6$ is

  • A
    $(1,-1,2)$
  • Correct answer
    B
    $(1,1,2)$
  • C
    $(-1,1,2)$
  • D
    $(1,1,-2)$

Solution

Equation of plane passes through the points $(1,-1,6),(0,0,7)$ and perpendicular to the plane $x-2 y+z=6$ is $$ \begin{aligned} & \left|\begin{array}{ccc} x-1 & y+1 & z-6 \\ 0-1 & 0+1 & 7-6 \\ 1 & -2 & 1 \end{array}\right|=0 \\ \Rightarrow \quad & \left|\begin{array}{ccc} x-1 & y+1 & z-6 \\ -1 & 1 & 1 \\ 1 & -2 & 1 \end{array}\right|=0 \\ \Rightarrow & (x-1)(1+2)-(y+1)(-1-1) \\ & +(z-6)(2-1)=0 \\ \Rightarrow \quad 3 x-3+2 y+2+z-6 & =0 \\ \Rightarrow \quad 3 x+2 y+z-7 & =0 \end{aligned} $$ This plane is passes through $(1,1,2)$.

Hence, the correct answer is option: 'B'.

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