Students in introductory physics struggle with vector algebra and cross product direction (CPD). While research into student understanding of vector algebra notes representation-dependence can impact student performance, with few exceptions these findings have not been applied to CPD questions or the use of right-hand rules (RHRs). A synthesis of the relevant literature yields four problem features likely to impact CPD understanding: the reasoning type required, the vectors' orientations, the need for parallel transport, and the physics context and features (or lack thereof). These categories form the basis of this study's exploration of the context- and representation-dependence of student performance on CPD questions.

The study analyzed 27 think-aloud interviews of second semester introductory physics students answering 80-100 CPD questions in different contexts and with varying problem features. Features were analyzed for correctness and responses were coded for the methods used and errors made.

The results reveal a wide variety of methods and RHRs, many types of errors, and significant context- and representation-dependence for problem features. Problems that required reasoning backward from a resultant presented the biggest challenge for students. Other performance issues stemmed from: 1) physical discomfort in the use of a RHR, 2) the plane of the given vectors, 3) the angle between the vectors, and, 4) misinterpretations of the into- and out-of- page symbols. The parallel transport issue did not appear to be nearly as prevalent for CPD as it is for vector addition and subtraction.

This study demonstrated that student difficulty with CPD is not as simple as misapplied RHRs. Student behavior is dependent on question context and its representation of various problem features. This study also confirmed earlier findings regarding difficulties with magnetic fields and forces and provided evidence of difficulties suspected but not yet explored.