In this article we investigate students' understanding of dot product as a projection. In the first part, we compare students' performance in three isomorphic multiple-choice problems: no-context, work and electric flux. We administered one of the three problems to 422 students who were in the process of completing required introductory physics courses. In the second part, we analyze the students' ability to connect the physical concepts with the dot product's formal representation. We carried out interviews with 14 students, in which they were asked to solve the same three isomorphic problems. Following the tests, we found a difference that was statistically significant: both physical context problems helped students select the projection interpretation option. However, the percentages of students that selected this option remained very low in the three problems. Moreover, during the interviews we noticed that students had serious difficulties in developing a coherent conceptual framework between the physical concepts and the dot product's formal representation.