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  4. The equation of the plane containing the line of intersection of the planes 2x-y=0 and y-3z=0 and perpendicular to the plane 4x+5y-3z-8=0 is

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Q. The equation of the plane containing the line of intersection of the planes $ 2x-y=0 $ and $ y-3z=0 $ and perpendicular to the plane $ 4x+5y-3z-8=0 $ is

Jharkhand CECEJharkhand CECE 2014

Solution:

Equation of plane containing the line of intersection of planes is
$ (2x-y)+\lambda (y-3z)=0 $ ... (i) Also, plane (i) is perpendicular to
$ 4x+5y-3z-8=0 $
$ \therefore $ $ 4(2)+5(\lambda -1)-3(-3\lambda )=0 $
$ \Rightarrow $ $ 14\lambda =-3 $
$ \Rightarrow $ $ \lambda =\frac{-3}{14} $
Putting the value of 'k in Eq. (i), we get
$ 28x-17y+9z=0 $ which is the required plane.