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 $4x+5y-3z=8$ is

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

Answer 1

Answer: (B)

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