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I have a line in 3D specified and bounded by its end points (x1, y1, z1) and (x2, y2, z2)

How do I calculate the minimum distance between the point and the line, keeping in mind that it may not be the perpendicular distance between the point and the extrapolated line because the line is bounded by its end points.

I would also like to know the point (x4, y4, z4) on the line that is closest to the external point.