# Vector Formalism in Introductory Physics VI: A Unified Solution for Simple Dot Product and Cross Product Equations

TL;DR: Simple vector dot products and cross products may be “undone” using formal methods consistent with Gibbsian vector algebra. Writing the cross product and dot product of an unknown vector relative to a given vector in a canonical form allows a well known vector identity to be used to isolate the unknown vector. Special cases […]

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# Vector Formalism in Introductory Physics IV: Unwrapping Cross Products Geometrically

TL;DR: Vector cross products are not like products of real numbers, for which there is an inverse operation to “undo” multiplication. I don’t think we should introduce cross products as a form of “multiplication” in introductory physics courses because it may reinforce the urge to “divide by a vector.” A better approach may be to […]

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# Vector Formalism in Introductory Physics III: Unwrapping Dot Products Geometrically

TL;DR: Vector dot products are not like products of real numbers, for which there is an inverse operation to “undo” multiplication. I don’t think we should introduce dot products as a form of “multiplication” in introductory physics courses because it may reinforce the urge to “divide by a vector.” A better approach may be to […]

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# Visualizing Eigenvectors with GlowScript

I owe this post entirely to my mathematics colleague Ethan Smith and his recent work on visualizing eigenvectors in a plane. This work is based in turn on the paper by Schoenfeld. I’ve taken the visualization to 3D with the help of GlowScript and Trinket. I was instantly interested in this project becuase I’m looking […]

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# Matter & Interactions I, Week 6

Note that I’m writing this one week late. This week we focused on getting used to GlowScript by doing all of the computational activities in chapter 1 of the textbook. Most everyone did fine. One student in particular is having significant difficulty because he is not a native English speaker. He tells me he wants […]

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# Matter & Interactions I, Week 1

This is the first post of a series of sixteen in which I will attempt to describe the weekly goings on in my introductory calculus-based physics course. You probably already know that I use Matter & Interactions for this course, and I have since 1999. In fact, I was the first instructor in North Carolina […]

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