The equation Ax + By + Cz = 0 represents the equation of a plane in 3-dimensional space. Each coefficient (A, B, and C) represents the normal vector to the plane. The equation can also be represented in vector form as N • P = D, where N is the normal vector, P is a point in the plane, and D is the distance from the plane to the origin.

When A, B, and C are all zero, this equation represents the degenerate case where the "plane" passes through the origin and is perpendicular to all axes, and thus all points on that plane are also on all three coordinate planes. In this case, the equation reduces to 0 = 0, which does not fully represent a distinct plane in 3D space.

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