Find the equation of the plane through the intersection of the planes `3x-4y+5z=10 and 2x+2y-3z=4` and parallel to the line `x=2y=3zdot`

Explanation

The equation of the plane passing through the intersection of the given planes is


`(3 x-4 y+5 z-10)+lambda(2 x+2 y-3 z-4)=0 `

`Rightarrow(3+2 lambda) x+(-4+2 lambda) y+(5-3 lambda) z-10-4 lambda=0 ldots(1)`

The given line is


`x=2 y=3 z`


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