Shortest Distance Between Skew Lines

The shortest distance between two skew lines can be calculated using the formula: where is the vector connecting a point on each line, and and are the direction vectors of the two lines.
Step 1:
Write the direction vectors and the point connecting the two lines. For the first line, the direction vector . For the second line, the direction vector . The connecting vector can be taken as the vector from the point on the first line to the point on the second line:
Step 2:
Compute the cross product : Expanding the determinant:
Step 3:
Compute the dot product :
Step 4:
Compute the magnitude of :
Step 5:
Finally, compute the shortest distance: