Question:
The equation of a plane containing the line of intersection of the planes $2 x-y-4=0$ and $y+2 z-4=0$ and passing through the point $(1,1,0)$ is :
Correct Option: , 3
Solution:
Let the equation of required plane be;
$(2 x-y-4)+\lambda(y+2 z-4)=0$
$\because$ This plane passes through the
point $(1,1,0)$ then $(2-1-4)+\lambda(1+0-4)=0$
$\Rightarrow \lambda=-1$
Then, equation of required plane is,
$(2 x-y-4)-(y+2 z-4)=0$
$\Rightarrow 2 x-2 y-2 z=0 \Rightarrow x-y-z=0$