Find 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 = 9.

Equation of plane through the line of intersection of planes in Cartesian form is

(1)


For the standard equation of planes,



So, putting in equation (1), we have


2x-y + λ(3z-y)=0


2x + (-1-λ)y + 3λz=0 (2)


Now as the plane is perpendicular the given plane,


For θ=90°, cos90°=0


(3)


On comparing with standard equations in Cartesian form,



Putting values in equation(3),


2.4 + (-1-λ).5 + 3λ.-3=0


8-5-5λ-9λ=0


-14λ=-3



Putting in equation(2)




28x-17y + 9z=0


So, required equation of plane is 28x-17y + 9z=0.


1