A recent study of calculus-based introductory physics students found that they performed significantly better on vector addition and subtraction tasks when the questions were given using the i jk representation instead of an "arrows-on-a-grid" representation, and also presented evidence that working knowledge of the i jk format was necessary to correctly perform vector operations in the arrow representation. A subsequent study found that algebra-based physics students also performed significantly better in the i jk representation than the arrow representation in both one- and two-dimensional problems, even though no explicit i jk instruction was given in the course. In this follow-up investigation we asked algebra-based physics students to reason physically about their answers, in order to assess if the higher performance on i jk questions indicates physical understanding or is the result of algorithmic "plug-and-chug" thinking. While students using i jk were more successful in computing the correct answer, their use of physical reasoning in justifying their answers was not significantly different than those using the arrow format. However, the higher number of students both correctly calculating and reasoning in the i jk format suggests that these students may benefit from i jk instruction.