Thread: Vector field in polar coordinates

1. Vector field in polar coordinates

I'm given $\displaystyle {\bold F}(r,{\theta}) = f(r,{\theta}){\bold u}_r + g(r,{\theta}){\bold u}_{\theta}$ where $\displaystyle {\bold u}_{\theta}$ and$\displaystyle {\bold u}_r$ are unit vectors.

$\displaystyle {\bold u}_r = \cos\theta{\hat i}+ \sin\theta{\hat j}$

$\displaystyle {\bold u}_{\theta} = -\sin\theta{\hat i}+ \cos\theta{\hat j}$

How do I rewrite $\displaystyle {\bold u}_r$ in vector form?

2. Re: Vector field in polar coordinates

okay, I just realized this is much easier than I thought. $\displaystyle {\v u}_r = < \cos\theta , \sin\theta >$