This study aimed to apply classical test theory (CTT) and Rasch analysis of item response theory (IRT) to investigate Thai participants' understanding of vectors and the characteristics of the test of understanding of vectors (TUV). A Thai version of the 20-items TUV was administered to 1,021 first-year science and engineering students at Prince of Songkla University, before and after common instructions. Although the engineering students (pre-score = 62%) had a significantly higher background of vectors than the science students (pre-score = 24%), proved by the effect size of Cohen's d, both groups have improved their learning into a medium level of the normalized gain (0.3 < < 0.7) after the instructions. Both groups improved the most with a vector representation concept. The participants were found to have the most difficulties with the unit vector and the cross product. However, the TUV is fairly easy for the assessed Thai first-year students. Overall, the item difficulty index derived from CTT was in moderate range (0.33-0.69). The difficulty index of the Thai-TUV obtained from CTT and Rasch analysis has a strong correlation indicating a reliable assessment tool.