Answer :

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.


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