A two-dimensional vector $\langle x,y \rangle$ has two variables, $x$ and $y$, and thus two degrees of freedom. If we convert it into its magnitude $m=||\langle x,y \rangle||$ and direction $\hat u=\widehat{\langle x,y \rangle}$, it seems that we have $m$ with one degree of freedom (since it is a scalar) and $\hat u$ with two degrees of freedom (since it is a vector). Is that correct? Explain whether there is a difference in degrees of freedom, and why or why not.