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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.