Calculating the distance between 2 straight lines in a 4d space?

The real answer would be- We dont know. We dont know what 4D space would be like. We are just creating assumptions and mathematical reasons to prove our calculations.

If youre given 2 distinct coordinates all you could do to calculate the magnitude of the distance is by finding the square root of the sum of the squares of the modulus of the difference between each respective coordinate.

If youre given non-parallel coplanar lines you can find the point of intersection. When theyre parallel you may be able to find the perpendicular distance by finding the modulus of coordinate differences. Since Cross products are not defined in 4D, im not sure if you can directly find shortest distance between two skew lines by knowing only their vectors.