The plane passing through the points


The plane passing through the points $(1,2,1),(2,1,2)$ and parallel to the line, $2 x=3 y, z=1$ also through the point:

  1. (1) $(0,6,-2)$

  2. (2) $(-2,0,1)$

  3. (3) $(0,-6,2)$

  4. (4) $(2,0,-1)$

Correct Option: , 2


Let plane passes through $(2,1,2)$ be


It also passes through $(1,2,1)$

$\therefore-a+b-c=0 \Rightarrow a-b+c=0$

The given line is

$\frac{x}{3}=\frac{y}{2}=\frac{z-1}{0}$ is parallel to plane

$\therefore 3 a+2 b+c(0)=0$

$\Rightarrow \frac{a}{0-2}=\frac{b}{3-0}=\frac{c}{2+3}$

$\Rightarrow \frac{a}{2}=\frac{b}{-3}=\frac{c}{2+3}$

$\Rightarrow \frac{a}{2}=\frac{b}{-3}=\frac{c}{-5}$

$\therefore$ plane is $2 x-4-3 y+3-5 z+10=0$

$\Rightarrow 2 x-3 y-5 z+9=0$

The plane satisfies the point $(-2,0,1)$.

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