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The phrase "direction in which" is correct and usable in written English.
You can use it to describe the way in which something is going or the way that an action is being taken. For example: "We need to find the proper direction in which to take our business in order to increase profits."
Exact(60)
These findings provide information on the direction in which efforts for improving intervention should be directed.
What matters now is the direction in which it changes.
Pick the direction in which the bomb isn't.
But look at the direction in which Isis are travelling.
Polarisation is the direction in which a light wave oscillates.
That's the direction in which MSNBC's coverage is heading.
The direction in which the vector curl B points is the direction in which A-1∫B·dl is largest.
This is the same direction in which all the planets orbit the sun.
The direction in which to compute the flux (e.g. X, Y, etcetera).
MIT biologists reveal how cells control the direction in which the genome is read.
Either way, it will give him a great direction in which to move his research.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com