ST_ShortestLine
Name
ST_ShortestLine — Returns the 2D shortest line between two geometries
Synopsis
    
     geometry
     
      ST_ShortestLine
     
     (
    
    geometry
    
     geom1
    
    , geometry
    
     geom2
    
    
     )
    
    ;
   
Description
   Returns the 2-dimensional shortest line between two geometries.
		The line returned starts in
   
    geom1
   
   and ends in
   
    geom2
   
   .
		If
   
    geom1
   
   and
   
    geom2
   
   intersect
        the result is a line with start and end at an intersection point.
		The length of the line is the same as
   
    ST_Distance
   
   returns for g1 and g2.
  
Availability: 1.5.0
Examples
    Shortest line between Point and LineString
SELECT ST_AsText(  ST_ShortestLine(
        'POINT (160 40)',
        'LINESTRING (10 30, 50 50, 30 110, 70 90, 180 140, 130 190)')
	) As sline;
---------------------------------------------------------
 LINESTRING(160 40,125.75342465753425 115.34246575342466)
  
    Shortest line between Polygons
SELECT ST_AsText( ST_ShortestLine(
         'POLYGON ((190 150, 20 10, 160 70, 190 150))',
         ST_Buffer('POINT(80 160)', 30)
              ) ) AS llinewkt;
-----------------
LINESTRING(131.59149149528952 101.89887534906197,101.21320343559644 138.78679656440357)