Question

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

• A. $(0,-6,2)$
• B. $(0,6,-2)$
• C. $(-2,0,1)$
• D. $(2,0,-1)$

Answer 1

The correct option is C $(-2,0,1)$

$L:\frac{x}{3}=\frac{y}{2}=\frac{z-1}{0}$
D.r.'s of line $(3,2,0)$
D.r.'s of line joining $A(1,2,1)$ and $B(2,1,2)$ is $(1,-1,1)$
If d.r.'s of plane is $(a,b,c)$ then
$3a+2b=0,a-b+c=0\Rightarrow a=-\frac{2}{5}c,b=\frac{3}{5}c$

$\therefore$ Plane :
$-2(x-1)+3(y-2)+5(z-1)=0$
$\Rightarrow -2x+3y+5z+2-6-5=0$
$\Rightarrow 2x-3y-5z=-9$
Hence plane will pass through $(-2,0,1)$