Find the plane equation which passes through point (1, - 1,1) and is perpendicular to two planes X-Y + Z = 1, 2x + y + Z + 1 = 0?

Find the plane equation which passes through point (1, - 1,1) and is perpendicular to two planes X-Y + Z = 1, 2x + y + Z + 1 = 0?

The normal vectors of the two planes are N1 = (1, - 1,1), N2 = (2,1,1),
So the direction vector of their intersection is N1 × N2 = (- 2,1,3),
This is also the normal vector of the plane perpendicular to both planes,
So the plane equation is - 2 (x-1) + (y + 1) + 3 (Z-1) = 0, which is reduced to 2x-y-3z = 0

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