A line in 3D is given by the parametric Vector

(1) 
The distance between a point on the line with parameter and the point is therefore

(2) 
To minimize the distance, take

(3) 

(4) 

(5) 
so the minimum distance is found by plugging (5) into (2) and taking the Square Root.
See also Line, Point, PointLine Distance2D
© 19969 Eric W. Weisstein
19990525