Question

The equation of a plane containing the line of intersection of the planes $2x-y-4=0$ and $y+2z-4=0$ and passing through the point $\left(1 , 1 , 0\right)$ is :

• A. $x+3y+z=4$
• B. $x-y-z=0$
• C. $x-3y-2z=-2$
• D. $2x-z=2$

Answer 1

Answer: (B)

The required plane is
$\left(2 x - y - 4\right)+\lambda \left(y + 2 z - 4\right)=0$
it passes through $\left(1 , 1 , 0\right)$
$\Rightarrow \left(2 - 1 - 4\right)+\lambda \left(1 - 4\right)=0$
$\Rightarrow -3-3\lambda =0\Rightarrow \lambda =-1$
$\Rightarrow x-y-z=0$