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In this article, we present our findings on STEM undergraduates’ understanding of the fundamental concepts of vectors. The study was conducted on a sample of 166 undergraduates who either had or had not taken a calculus-based introductory physics course at a comprehensive private university in the USA. A quiz about vectors on both the algebraic aspects (with the coordinations for the head and tail of a vector and with unit vector notation) and geometric aspects (with arrow notation), along with a survey of their prior experience regarding vectors, was given. The results revealed that several learning difficulties are due to a lack of understanding of the connections between the algebraic and geometric aspects of vectors. This underlines the need for the implementation of effective teaching strategies that would better emphasize the connections between the algebraic and geometric aspects of vectors. [ABSTRACT FROM AUTHOR]