Determine the equation of a plane, P3, that intersects the planes P1: x + y + 3z - 2 = 0 and P2: x - y + 2z = 0

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There can be infinite number of planes that intersect the planes P1: x + y + 3z - 2 = 0 and P2: x - y + 2z = 0.

The required plane should not be parallel to x + y + 3z = 2 or the vector < 1,...

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There can be infinite number of planes that intersect the planes P1: x + y + 3z - 2 = 0 and P2: x - y + 2z = 0.

The required plane should not be parallel to x + y + 3z = 2 or the vector < 1, 1, 3> should not be a normal vector of P3. Also, the vector should not be parallel to x - y + 2z = 0 or the vector < 1 -1 2 > should not be a normal vector of P3. A plane with any other normal vector, for example < 1 1 1 > intersects both P1 as well as P2.

One example of the infinite number of planes that intersect both P1 and P2 is x + y + z = 0

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