The plane equation of the straight line x + y + Z = 0, x + 2y-2z + 1 = 0 and parallel to the straight line x-2y-2 = 0, x-3z + 15 = 0 is solved,

The plane pencil equation passing through the lines X + y + Z = 0 and X + 2y-2z + 1 = 0 is x + y + Z + a (x + 2y-2z + 1) = 0, where a is a parameter, i.e. (1 + a) x + (1 + 2a) y + (1-2a) Z + 1 + a = 0. The plane a is parallel to the line x-2y-2 = 0, x-3z + 15 = 0, and the vector r obtained by (1, - 2,0) cross multiplication (1,0, - 3) = (6,3,2) plane

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