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 $