The complete question is below because the world limit doesn't allow me to post full question in title.
Find the shortest distance between the straight line joining the points A(3,2,-4) and B(1,6,-6) and the straight line joining the points C(-1,1,-2) and D(-3,1,-6). Also find equation of the line of shortest distance and coordinates of the feet of the common perpendicular
I have found the shortest distance by two methods
by determining that lines are skew and proceeding further on e.g. taking dot product with direction vectors and then by finding s and t. Then I found the direction vector and thus by finding its magnitude of that direction vector I got the shortest distance
by finding equation of parallel planes and by solving them using distance formula between two planes
In both cases, I got shortest distance equals to sqrt(21). [is it right]
But my real query is how to find equation of the line of shortest distance and coordinates of the feet of the common perpendicular. Please help.