# Polar vector coordinates

1. Sep 2, 2007

### ice109

i dont understand the point of $\hat{\theta}$ if a vector is completely described by $\textbf{r}=r \hat{\textbf{r}}$

btw tex is doing something weird, apparently i can't make greek letters bold
$$\textbf{\delta}$$

2. Sep 2, 2007

### ice109

no one of you math geniuses can answer this for me?

3. Sep 3, 2007

### HallsofIvy

I don't pretend to be a math genius but perhaps none of them understands your question. What do you mean by "a vector is completely described by $\textbf{r}=r \hat{\textbf{r}}$". Are you talking about a specific vector? Because that certainly does not "completely describe" a general vector. If you have a vector "completely described" by $\textbf{r}=r \hat{\textbf{r}}$ then you don't need $\theta'$.

If you have formulas for both r' and $\theta'$, what makes you think that the vector is "completely described" by $\textbf{r}=r \hat{\textbf{r}}$
? Perhaps it would help if you stated the precise problem.

4. Sep 3, 2007

### learningphysics

$$\hat{\textbf{r}}[/itex] depends on [tex]\theta$$... It changes according to the angle. Unless you know what $$\theta$$ is you can't draw [tex]\hat{\textbf{r}}[/itex]

5. Sep 3, 2007

### ice109

does $\textbf{r}$ describe a general vector in cartesian coordinates? if it does then i don't see any difference between the position vector in cartesian coordinates and in polar coordinates.

in fact i don't even understand the physical meaning of a linear combination of $\hat{\textbf{r}}$ and $\hat{\theta}$. actually that is erroneous , i have no problem visualizing the resultant of these two vectors, i would just need to connect them head to tail. what i don't understand is what i said before, what is the point of the $\hat{\theta}}$

the picture represents my understanding of the the polar coordinates in terms of the cartesian coordinates where $\textbf{A}$ is the vector i'm trying to describe in terms of the the polar unit vectors. is it correct? and if it is correct why can't describe $\textbf{A}$ by just scaling the $\hat{\textbf{r}}$ a little and making its $\theta$ argument little bigger?

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