Suppose I have a vector $\overrightarrow{a}$. If I wanted to describe its magnitude, there's a standard notation for that, $\lVert\overrightarrow{a}\rVert$. Is there a standard notation for its orientation?
I know that I break up the vector into its horizontal and vertical components, I can express the angle as $\theta=\arctan\frac{\lVert\overrightarrow{a_y}\rVert}{\lVert\overrightarrow{a_x}\rVert}$, but the notation is awfully cumbersome to write that way, not to mention that for this to work in all quadrants I’d need to use signed magnitude, almost an oxymoron.
Some have suggested appealing to unit vectors, where $\mathbf{\hat{a}}=\frac{\overrightarrow{a}}{\lVert\overrightarrow{a}\rVert}$, but that’s just kicking the can down the road. It’s fine to say that $\overrightarrow{a}$ and $\mathbf{\hat{a}}$ have the same orientation, but they’re still both vectors, even if the unit vector’s magnitude is $1$; I can’t just write $\mathbf{\hat{a}}=\theta$.
What I’ve been using thus far in my notes is $\overrightarrow{a_\theta}$, figuring that if the $x$ and $y$ components can be written as $\overrightarrow{a_x}$ and $\overrightarrow{a_y}$, then a similar notation could be used to denote the angle component of the vector. I gather that’s not standard notation, however, hence my question.
Hat notation is probably what you're after $$\hat{a} = \frac{\vec{a}}{\|\vec{a}\|} .$$