Shortest distance between two skew lines in 3D space. 

also here's code if someone will be in need to: public static void ClosestPointsOnTwoLines(Vector3 Origin1, Vector3 Direction1, Vector3 Origin2, Vector3 Direction2, out Vector3 closestPointLine1, out Vector3 closestPointLine2){ closestPointLine1 = Vector3.zero; closestPointLine2 = Vector3.zero; float a = Vector3.Dot(Direction1, Direction1); float b = Vector3.Dot(Direction1, Direction2); float e = Vector3.Dot(Direction2, Direction2); float d = a*e - b*b; // if lines are not parallel if(d != 0){ Vector3 r = Origin1 - Origin2; float c = Vector3.Dot(Direction1, r); float f = Vector3.Dot(Direction2, r); float s = (b*f - c*e) / d; float t = (a*f - c*b) / d; closestPointLine1 = Origin1 + Direction1 * s; closestPointLine2 = Origin2 + Direction2 * t; } } this is code using Unity 3D engine C# language witch is similar to C#/C/C++

it´s the same thing. he is checking where the cross product is zero.

Jorgen Bengtsson Cross product is a vector so it can't equal a scalar. You mean where dot product is 0

The shortest distance to a line is the path perpendicular to the line from any point. The corresponding points on each line at the shortest distance must therefore both be on a line perpendicular to the other.