The equation of a plane containing the line of intersection of the planes $2 \mathrm{x}-\mathrm{y}-4=0$ and…
The equation of a plane containing the line of intersection of the planes $2 \mathrm{x}-\mathrm{y}-4=0$ and $\mathrm{y}+2 \mathrm{z}-4=0$ and passing through the point $(1,1,0)$ is
$x-y-z=0$
$2 x-z=2$
$x-3 y-2 z=-2$
$x+3 y+z=4$
Solution
The equation of plane containing the line of intersection of the planes
$2 x-y-4=0$ and $y+2 z-4=0$ is
$(2 x-y-4)+\lambda(y+2 z-4)=0$
But it passes through $(1,1,0)$
$\Rightarrow \lambda=-1$
$\Rightarrow$ The required equation of plane is
$\begin{aligned} & (2 x-y-4)-(y+2 z-4)=0 \\ & \Rightarrow 2 x-2 y-2 z=0 \\ & \Rightarrow x-y-z=0\end{aligned}$