Let the plane containing the line of intersection of the planes \(P_1: x+(\lambda+4) y+z=1\) and \(P_2: 2 x+y+z=2\) pass…

Let the plane containing the line of intersection of the planes \(P_1: x+(\lambda+4) y+z=1\) and
\(P_2: 2 x+y+z=2\) pass through the points \((0,1,0)\) and \((1,0,1)\). Then the distance of the point \((2 \lambda, \lambda,-\lambda)\) from the plane \(P_2\) is