An Efficient Vector-Intensive Presentation of 2-Dimensional Curves

This paper introduces notation for finding by inspection the vector v-perp obtained by rotating a 2-space vector v counterclockwise by 90o. Perp vectors facilitate the use of the projections needed to present curvature and to obtain orthogonal decompositions of the velocity and acceleration vectors that describe motion along polar as well as rectangular curves. They also reveal a duality relationship between 2-dimensional divergence and curl that enhances the presentation and understanding of Green’s Theorems. Overall, perp vectors enable the vector methods used to describe curvature and motion in space to be introduced first in the plane, where they are easily visualized and drawn.