Comments on Solely by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{limegreen}{|\vec{b}| - |\vec{r}|}$ ?
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Solely by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{limegreen}{|\vec{b}| - |\vec{r}|}$ ?
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Yearly, I teach 16 year olds the diagram beneath (improvement of this original) that reappears on standardized tests with different letters, orientation, position of the vectors. Tests require students to distinguish and label $\color{red}{\vec{b} - \vec{r}}$ vs. $\color{limegreen}{|\vec{b}| - |\vec{r}|}$. Despite my best endeavors, someone ALWAYS mixes them red and green, whenever this diagram resurfaces on tests!
How do you best explain their pictoric difference? How would you prevent this diagrammatic mix up BY EYE?
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