Student understanding of vector products: The effects of context and experience

As part of an ongoing investigation of student understanding of vectors, vector operations, and their physical interpretations, we present findings from responses to survey questions about the magnitude and direction of vector products in different contexts, asked to students at different class levels. The contexts include mathematics with no physics applied, mechanical work, flux of a uniform magnetic or electric field, and magnetic force on a charged particle. This pseudo-longitudinal study included students enrolled in introductory calculus-based physics, a sophomore-level mathematical methods in physics course, and two junior-level electricity and magnetism courses. Between 12% and 30% of introductory students correctly answered that the result of a dot product does not have a direction across all the different contexts. The most common incorrect responses were that the dot product points in a direction between the two vectors in the mathematics context and that the direction of the work is in the same direction as the displacement. Performance improves as the class level increases.