Consider the unit vectors (hat{mathbf{x}}, hat{mathbf{y}}, hat{mathbf{r}}), and (hat{boldsymbol{theta}}) in a plane. (a) Find (hat{mathbf{r}}) and (hat{boldsymbol{theta}})
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Consider the unit vectors \(\hat{\mathbf{x}}, \hat{\mathbf{y}}, \hat{\mathbf{r}}\), and \(\hat{\boldsymbol{\theta}}\) in a plane.
(a) Find \(\hat{\mathbf{r}}\) and \(\hat{\boldsymbol{\theta}}\) in terms of any or all of \(\hat{\mathbf{x}}, \hat{\mathbf{y}}, x\), and \(y\).
(b) Find \(\hat{\mathbf{x}}\) and \(\hat{\mathbf{y}}\) in terms of any or all of \(\hat{\mathbf{r}}, \hat{\boldsymbol{\theta}}, r\), and \(\theta\).
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