Expression

• -abcdefg $\displaystyle {\left|\vec{{a}}\times\vec{{b}}\right|}$
• -abcdefg The arc length function
• -abcdefg The unit normal vector
• -abcdefg The length of a curve
• -abcdefg The unit tangent vector
• -abcdefg $\displaystyle \vec{{a}}.\vec{{b}}$
• -abcdefg The curvature

Formula

1. $\displaystyle {\int_{{a}}^{{t}}}{\left|{r}'{\left({u}\right)}\right|}{d}{u}$
2. $\displaystyle \frac{{\vec{{r}}'{\left({t}\right)}}}{{\left|\vec{{r}}'{\left({t}\right)}\right|}}$
3. $\displaystyle {\left|\vec{{a}}\right|}{\left|\vec{{b}}\right|}{\sin{{\left(\theta\right)}}}$
4. $\displaystyle \frac{{\vec{{T}}'{\left({t}\right)}}}{{\left|\vec{{T}}'{\left({t}\right)}\right|}}$
5. $\displaystyle {\left|\vec{{a}}\right|}{\left|\vec{{b}}\right|}{\cos{{\left(\theta\right)}}}$
6. $\displaystyle {\int_{{a}}^{{b}}}{\left|{r}'{\left({t}\right)}\right|}{\left.{d}{t}\right.}$
7. $\displaystyle \frac{{{\left|\vec{{r}}{\left({t}\right)}\times\vec{{r}}'{\left({t}\right)}\right|}}}{{\left|\vec{{r}}'{\left({t}\right)}\right|}^{{3}}}$