Is there any established notation to abbreviate $\vec{x}/||\vec{x}|| = \frac{\vec{x}}{||\vec{x}||}$? Sure, this expression looks quite short already, but with a long argument such as $\vec{x} = a\cdot (\vec{b} \times \vec{c}) - (\vec{c} \cdot \vec{d}) \cdot \vec{e} + \frac{\vec{f} \cdot \vec{g}}{||\vec{f}|| \cdot ||\vec{g}||} \cdot \vec{h} + \dots$ it becomes hard to read very fast. I am thinking of something as $(\vec{x})_u$ or so.
Such a notation would not only simplify $\vec{x}/||\vec{x}||$, but also the $\frac{\vec{f} \cdot \vec{g}}{||\vec{f}||\cdot||\vec{g}||}$ in the argument $\vec{x}$. Also, repeating the same long expression is not too polite, since a reader might feel the need to look for small, but significant differences between the nominator and the denominator.
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$\begingroup$If you switch to using boldface font for vectors, e.g., $\mathbf x$ rather than $\vec x$, then it is reasonable (and common in physics/engineering circles) to use the notation $$\hat{\mathbf x}=\frac{\mathbf x}{\|\mathbf x\|}$$ It's right at the beginning of the Wikipedia article Unit vector.
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