Skew lines and what's between them Is it always possible to find a line perpendicular to two skew lines in space?
And how can we visualise the proof geometrically? And if anyone could present the proof that it is always possible to exist a line perpendicular to both skew lines, please elaborate.

Think about how you would find the shortest distance between the two lines. You know that the shortest distance from a line to a point not on the line is along a segment that’s perpendicular to the line. By symmetry, this means that the shortest distance between two skew lines must be along a segment that’s perpendicular to both of them.
