Drawing absolute value bars around a fraction with different height of numerator and denominator

Question

I would like to typeset the absolute value of a fraction, e. g.

with absolute value bars that are shorter at the bottom, like in

Is there any way in LaTeX to achieve this rather than the first example?

Details:

I am calculating the angle between two lines in three-dimensional space with the following formula:

This looks really nice. But when I now substitute the coordinates of the vectors like this:

\cos\phi=\left|\frac{
        \begin{pmatrix}1\\1\\1\end{pmatrix}
    \circ
        \begin{pmatrix}1\\2\\3\end{pmatrix}
    }{
        \sqrt3\cdot\sqrt{1^2+2^2+3^2}
    }\right|

I get the following result:

Yuck! There is way too much space below the fraction inside the absoulte value bars!

I already tried using \Biggl| and \Biggr:

\cos\phi=\Biggl|\frac{
        \begin{pmatrix}1\\1\\1\end{pmatrix}
    \circ
        \begin{pmatrix}1\\2\\3\end{pmatrix}
    }{
        \sqrt3\cdot\sqrt{1^2+2^2+3^2}
    }\Biggr|

but that only yields a somewhat acceptable, but slightly incorrect result:

Answer 1

Here, I use \stretchleftright{|}{...}{|} to achieve it.

\documentclass{article} 
\usepackage{scalerel,amsmath}
\begin{document} 
\[
\cos\phi=\stretchleftright{|}{\frac{
        \begin{pmatrix}1\\1\\1\end{pmatrix}
    \circ
        \begin{pmatrix}1\\2\\3\end{pmatrix}
    }{
        \sqrt3\cdot\sqrt{1^2+2^2+3^2}
    }}{|} 
\]
\end{document}

Answer 2

I'd like to suggest a solution that's different from either of your preferred choices.

\documentclass{article}
\usepackage{mathtools} % for '\DeclarePairedDelimiter' macro
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

\begin{document}
\[
\cos\phi= \frac{1}{\sqrt3 \cdot\sqrt{1^2+2^2+3^2}}
          \abs*{\begin{pmatrix}1\\1\\1\end{pmatrix}\circ
                \begin{pmatrix}1\\2\\3\end{pmatrix}}  
\]
\end{document}