How do you prove two planes are the same?
How do you prove two planes are the same? This is called the vector equation of the plane. Two planes n1 ·(r-a1) = 0 and n1 ·(r-a2) = 0 are parallel if and only if their normal vectors n1 and n2 are parallel or opposite. If two planes are parallel then they either intersect everywhere (they're the same plane) or they don't intersect at all.
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