The test of understanding of vectors (TUV) is a multiple-choice test that was recently developed to assess student understanding of vector concepts required in introductory physics courses at the university level. In this study, the TUV was administered to 889 first-year students at the University of Zagreb. The Rasch model was used to evaluate the functioning of the TUV, and to determine the difficulty scale of vector concepts evaluated by this assessment instrument. The results of the Rasch analysis showed a good functioning of test items. However, the TUV was not well targeted to our sample of first-year engineering and science students in introductory physics courses. About half of the students had abilities outside the range of item difficulties, indicating that the TUV would benefit from including more difficult items that would help to better estimate the abilities of these students. Further analysis of the data from subpopulations in our sample showed that the TUV can be well targeted for certain student populations. Students’ scores suggest that the most difficult vector concept tested by the TUV is the unit vector, followed by the cross product, subtraction of vectors, dot product, and direction of a vector.