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No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.
Two dimensional geometry is called "plane geometry" meaning that it occurs on a single surface or plane. The objects used in plane geometry are called plane figures.
A parabola is a curved shape that is plotted on the Cartesian plane.
A flat surface with two dimensional shape.
In a plane, each vector has only one orthogonal vector (well, two, if you count the negative of one of them). Are you sure you don't mean the normal vector which is orthogonal but outside the plane (in fact, orthogonal to the plane itself)?