Distance between skew lines

Find the distance between line r through P(3, 12, 9) with direction (5, 4, 5) and line s through Q(11, 10, 12) with direction (3, 3, 7).

Step-by-step solution

First check the relative position: if they meet, the distance is 0; if they are parallel, it is the distance from a point to the other line.
For skew lines, draw the plane that contains one and is parallel to the other.
The distance is that of a point of the second line to that plane.
The common perpendicular meets both lines at points A and B.

Result: A(9.32, 17.06, 15.32) and B(12.76, 11.76, 16.12); distance = 6.36 units.

Two skew lines have no common point: the distance is measured along the common perpendicular, not between their projections.