The concept of vector plays a central role in engineering mechanics and strength of materials, where many quantities are vectorial in nature. Phenomenographic studies can be useful in revealing the different perspectives of the students’ understanding of vectors and variation theory is a promising approach to improve the teaching of vectors. In this study, we will use the frameworks of phenomenography and variation theory to explore students’ understanding and difficulties in using the concept of vector. The data consists of pre-, post- and delayed post-tests questions about vectors as well as student project reports in the course “Models, Mechanics & Materials”, given to first-year engineering students, studying “Sustainable Design” at Aalborg University, Copenhagen, Denmark. The results of the pre-test suggest that most emphasis in teaching vectors in upper secondary school mathematics has been on the algebraic representations of vectors and less on their graphical representations, the mastery of which is essential to succeed in engineering courses such as mechanics and strength of materials. The results of the post- and delayed post-tests as well as the students’ project reports showed some improvement in the students’ performances after using variation- and context-based teaching of vectors in the course. The article concludes with some proposals on how the results of this study can be used to enhance the teaching and learning of vectors at the upper secondary schools and the university.