When the geoid and ellipsoid coincide, the datum origin is established. The normal to the ellipsoid coincides with which of the following at the datum origin?

At the datum origin where the geoid and ellipsoid coincide, the normal to the ellipsoid is aligned with the plumb line. The plumb line represents the direction of gravity, which is pivotal for establishing verticality in geodesy. It points directly towards the center of the Earth, thus indicating the direction that would be considered "down" in a local context.

When we establish a geodetic datum, the alignment at the datum origin means that the surface of the ellipsoid (a mathematical model of the Earth's shape) is tangent to the geoid (the surface representing mean sea level under the influence of Earth's gravitational field) at that point. Since the ellipsoid is a smooth surface that models the Earth's shape, the normal line (or perpendicular line) at this point aligns with the local plumb line. This is fundamental for accurately determining elevations and ensuring that measurements reflect true vertical paths.

The other concepts mentioned, such as the horizontal plane, geoid, and vertical plane, don't accurately describe this precise relationship at the point of coincidence. The horizontal plane is a level surface that is orthogonal to the direction of gravity, but it does not coincide with the normal direction at the datum origin. Similarly, the geoid is the reference