Q101 / 160 · TS EAMCET 2023 (13 May Shift 2) · Mathematics

A plane $\pi$ passing through the point $(1,1,1)$ is perpendicular to the line joining the points $(6,3,2)$ and $(1,-4,-9)$. If $a x+b y+c z-23=0$ is the equation of the plane $\pi$ then $\mathrm{a}+\mathrm{b}-\mathrm{c}=$

  • Correct answer
    A
    1
  • B
    23
  • C
    9
  • D
    13

Solution

D.R. of line joining points $(6,3,2)$ and $(1,-4,-9)$ is $(5,7,11)$ $\therefore \quad$ Equation of plane is $$ \begin{aligned} & 5(x-1)+7(y-1)+11(z-1)=0 \\ \Rightarrow & 5 x+7 y+11 z-23=0 \\ \therefore \quad & a=5, b=7, c=11 \\ \Rightarrow & a+b-c=5+7-11=1 . \end{aligned} $$

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

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