Question

The equation of the plane passing through the origin and containing the line of intersection of the planes $5x+y-3z=2$ and $x+2y+3z=1$ is

• A. $2x+y=1$
• B. $x-y-3z=0$
• C. $4x-y-6z=0$
• D. $7x+5y+3z=0$

Answer 1

The correct option is B $x-y-3z=0$

The equation of the plane containing the line of intersection of the planes $5x+y-3z=2$ and $x+2y+3z=1$ is of the form $P_1+\lambda P_2=0$
$\Rightarrow (5x+y-3z-2)+\lambda (x+2y+3z-1)=0$
But, above plane passes through origin.
$\Rightarrow \lambda =-2$
$\therefore$ Required plane equation is $x-y-3z=0$
Hence, option B.