Q. 15.0( 1 Vote )

Find the equation

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


x + y + z-6 + λ(2x + 2y + 4z + 5)=0


(1 + 2λ)x + (1 + 2λ)y + (1 + 4λ)z-6 + 5λ=0 (2)


Now plane passes through (1,1,1) then it must satisfy the plane equation,


(1 + 2λ).1 + (1 + 2λ).1 + (1 + 4λ).1-6 + 5λ=0


1 + 2λ + 1 + 2λ + 1 + 4λ-6 + 5λ=0


3 + 8λ-6 + 5λ=0


13λ=3



Putting in equation (2)




19x + 19y + 25z-63=0


So, the required equation of plane is 19x + 19y + 25z=63.


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