# Vector calculus: Arclength

Let $u_1 = (x+y)/2$ and $u_2 = (x-y)/2$, where $x$ and $y$ are Cartesian coordinates. Write the differential $d \vec{r}$ as a linear combination of $\hat{e}_1$ and $\hat{e}_2$, and determine the element $ds$ (or $ds/dt$) of arclength.