Your proposed title is
Showing $\frac{|\overrightarrow{A_1B}|}{|\overrightarrow{A_1C}|}\frac{|\overrightarrow{B_1C}|}{|\overrightarrow{B_1A}|}\frac{|\overrightarrow{C_1A}|}{|\overrightarrow{C_1B}|}=1$ implies $AA_1$, $BB_1$, $CC_1$ concur
(215 characters).
Since \newcommand
is now local, I believe it is safe to do [Edit: as per Martin's comment, this may not be so safe]
Showing $\newcommand\Y[3]{\frac{|\overrightarrow{#1_1#2}|}{|\overrightarrow{#1_1#3}|}}\Y ABC\Y BCA\Y CAB=1$ implies $AA_1$, $BB_1$, $CC_1$ concur
(145 characters, under the 150 limit)
The MathJax result is the same: yours is
Showing $\frac{|\overrightarrow{A_1B}|}{|\overrightarrow{A_1C}|}\frac{|\overrightarrow{B_1C}|}{|\overrightarrow{B_1A}|}\frac{|\overrightarrow{C_1A}|}{|\overrightarrow{C_1B}|}=1$ implies $AA_1$, $BB_1$, $CC_1$ concur
Mine is
Showing $\newcommand\Y[3]{\frac{|\overrightarrow{#1_1#2}|}{|\overrightarrow{#1_1#3}|}}\Y ABC\Y BCA\Y CAB=1$ implies $AA_1$, $BB_1$, $CC_1$ concur
If you want to slightly mess the formatting, you can replace the three $, $
s with \
for 3 more characters.
PS the frustration is not unwarranted but the website designer(s) likely had to work around certain compromises; not assuming their lack of understanding would perhaps result is less downvotes (not that it matters, in meta of all places).
\vec
while you use\overrightarrow
and that's why I asked if you suggest an "alternative". (3) I'm one of those who upvoted this post; this is of course not relevant to your question though. $\endgroup$