  In this paper, we discuss four errors introductory physics students make when
attempting to add two inverse-square law vectors. We observe multiple instances
in which students 1) add vectors as if they were scalars, 2) project the $r$
(or $r^2$) in the denominator, instead of the entire vector, when attempting to
find the vector's components, 3) incorrectly apply the Pythagorean theorem when
attempting to calculate the magnitude of the resultant vector, and 4)
incorrectly relate the signs of the components of an electric field (or force)
to the signs of the electric charges. While these are not the only errors
students make, they are the most frequently occurring based on our analysis of
678 exams taken by students in either introductory mechanics or electricity and
magnetism (E&M). We then show how these errors can be encoded into a new type
of activity or assessment question which we call a ``student error task."
Introductory physics instructors can use the student error task in this paper
as a way to engage or assess their students' understandings of how to add two
inverse-square law vectors.
