- #1
LagrangeEuler
- 717
- 20
## \vec{r}=\rho \cos \varphi \vec{i}+\rho \sin \varphi \vec{j}+z\vec{k} ##
we get
[tex]\vec{e}_{\rho}=\frac{\frac{\partial \vec{r}}{\partial \rho}}{|\frac{\partial \vec{r}}{\partial \rho}|}[/tex]
[tex]\vec{e}_{\varphi}=\frac{\frac{\partial \vec{r}}{\partial \varphi}}{|\frac{\partial \vec{r}}{\partial \varphi}|}[/tex]
Is it correct for any orthogonal system or maybe for any system? Why you can use this relation?
we get
[tex]\vec{e}_{\rho}=\frac{\frac{\partial \vec{r}}{\partial \rho}}{|\frac{\partial \vec{r}}{\partial \rho}|}[/tex]
[tex]\vec{e}_{\varphi}=\frac{\frac{\partial \vec{r}}{\partial \varphi}}{|\frac{\partial \vec{r}}{\partial \varphi}|}[/tex]
Is it correct for any orthogonal system or maybe for any system? Why you can use this relation?