Question:
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:
Correct Option: , 2
Solution:
Let plane passes through $(2,1,2)$ be
$a(x-2)+b(y-1)+(z-2)=0$
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 $(-2,0,1)$.