Answer :

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

(1)


For the standard equation of planes in Cartesian form



So, putting in equation 1 we have


x + 2y + 3 z-5 + λ(3x -2y -z + 1)=0


(1 + 3λ)x + (2-2λ)y + (3-λ)z-5 + λ=0


Now equation of plane in intercept form



As given equal intercept means a=c


First, we transform equation of a plane in intercept form




On comparing with the standard equation of a plane in intercept form



Now as a=b=c




Putting in equation (2), we have




5x + 2y + 5z-9=0


5x + 2y + 5z=9


So, required equation of plane is 5x + 2y + 5z=9.


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