Nearest points

Expressing the two lines as vectors:

:
:

The cross product of and is perpendicular to the lines.

The plane formed by the translations of Line 2 along contains the point and is perpendicular to .

Therefore, the intersecting point of Line 1 with the above-mentioned plane, which is also the point on Line 1 that is nearest to Line 2 is given by

Similarly, the point on Line 2 nearest to Line 1 is given