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 $(1,1,0)$ is:

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

Answer 1

The correct option is A $x-y-z=0$

Let equation of planes be $P_1$ and $P_2$
Now according to question,
$\Rightarrow P_1+\lambda P_2=0$
$\Rightarrow (2x-y-4)+\lambda (y+2z-4)=0...\left(1\right)$

The plane passes through the point $(1,1,0)$
Put $(1,1,0)$ in equation $\left(1\right)$
$\Rightarrow 1+\lambda =0\Rightarrow \lambda =-1$
$\therefore x-y-z=0$