Which relation is not defined for the two segments shown?

When considering the relationships between two line segments, it's important to understand the definitions of each relation.

The parallel relation implies that two lines run alongside each other at a constant distance apart and do not intersect. This is always defined for segments that are oriented in such a way.

The perpendicular relationship indicates that two segments intersect at a right angle (90 degrees). If the segments cross each other in this way, this relation is applicable and can be defined.

The coincident relation indicates that two line segments or lines occupy the same space, meaning one segment rests directly on top of the other. This is definable when segments overlap.

However, the collinear relation specifically refers to segments that lie on the same line, which requires the segments to be in a straight line extending in both directions. If the segments do not lie along the same infinite line yet may still be oriented in some other way (like intersecting or parallel), they cannot be termed as collinear.

Thus, within the given context, the relation that is not defined for the two segments is collinear, as it necessitates both segments being perfectly aligned.