Looking on the internet deeply has found these results:

in this direction is the most popular phrase on the web.

on this direction 114,200 results on the web	in this direction 11,270,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	The SILOL redesign goes in this direction . Efforts must continue in this direction. Our commitment must be to insist concretely in this direction. The recently published Handbook on Environmental Public Procurement contributes significantly in this direction. The R8 has taken a further step in this direction . For us development in this direction is unacceptable. Americans are exaggerating with their tranquillity in this direction. Our group has tabled several amendments in this direction.

on this direction

114,200 results on the web

in this direction

11,270,000,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

The SILOL redesign goes in this direction .
Efforts must continue in this direction.
Our commitment must be to insist concretely in this direction.
The recently published Handbook on Environmental Public Procurement contributes significantly in this direction.
The R8 has taken a further step in this direction .
For us development in this direction is unacceptable.
Americans are exaggerating with their tranquillity in this direction.
Our group has tabled several amendments in this direction.