Student handout: The Distance Formula (Star Trek)

Static Fields 2024 (8 years)
A short improvisational role-playing skit based on the Star Trek series in which students explore the definition and notation for position vectors, the importance of choosing an origin, and the geometric nature of the distance formula. \[\vert\vec{r}-\vec{r}^\prime\vert=\sqrt{(x-x^\prime)^2+(y-y^\prime)^2-(z-z^\prime)^2}\]
What students learn
  • Position vectors are needed to locate an object in space relative to an origin;
  • The distance between two objects, determined by the formula \(\vert\vec{r}-\vec{r^{\prime}}\vert\) is independent of origin and coordinates;
  • A coordinate dependent expression for the distance formula \(\vert\vec{r}-\vec{r^{\prime}}\vert=\sqrt{(x-x^{\prime})^2 + (y-y^{\prime})^2 }\) is equivalent to the Pythagorean Theorem.

Find a coordinate independent expression for the distance between two points and then evaluate it in rectangular coordinates.


Author Information
Corinne Manogue
Keywords
distance formula coordinate systems dot product vector addition
Learning Outcomes