Question

The equation of the plane passing through the line of intersection of the planes $2x-y=0$ and $3z-y=0$ and perpendicular to the plane $4x+Sy-3z=8$ is

• A. $2x+17y+9z=0$
• B. $28x-17y+9z=0$
• C. $2x+17y-9z=0$
• D. None of these

Answer 1

The correct option is B $28x-17y+9z=0$

The equation of plane passing through the intersection line of the planes $2x-y=0$ and $3z-y=0$ is
$(2x-y)+\lambda (3z-y)=0$
$2x-(1+\lambda )y+3\lambda z=0$ .....(i)
According to the question, plane (i) will be perpendicular to
$4x+Sy-3z=8$ .....(ii)
Therefore, $2.4-(1+\lambda )5+3\lambda (-3)=0$
$\Rightarrow 8-5-5\lambda -9\lambda =0$
$\Rightarrow 14\lambda =3\Rightarrow \lambda =\frac{3}{14}$
Thus, required plane is
$(2x-y)+\frac{3}{14}(3z-y)=0$
$\Rightarrow 28x-17y+9z=0$