How to find the shortest distance between two skew lines using vector math.

[Yehoshua18]

Hey, I've been trying to figure out how to find the shortest distance between two skew lines. I can do it in C# without using AutoCAD vectors, but it would be much more simple if I could use them. Any idea how to make it happen? Thanks!

https://www.toppr.com/guides/maths/three-dimensional-geometry/distance-between-skew-lines/

[Yehoshua18 · Accepted solution]

I figured it out. Just incase anyone ever needs this, here is the solution.

public static void Interference(Line L1, Line L2)
        {
            Document doc = Application.DocumentManager.MdiActiveDocument;
            Database db = doc.Database;

            Vector3d U1 = L1.StartPoint.GetVectorTo(L1.EndPoint);
            Vector3d U2 = L2.StartPoint.GetVectorTo(L2.EndPoint);
 
            Vector3d N = U1.CrossProduct(U2);

            double nmag = N.Length;

            Vector3d P1P2 = L1.StartPoint.GetVectorTo(L2.StartPoint);

            Double Distance = Math.Abs(P1P2.DotProduct(N)/nmag);

            doc.Editor.WriteMessage(string.Format("\n Minimum Distance between lines {0} =",Distance.ToString()));
        }