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The phrase "a given direction" is correct and usable in written English.
It can be used when referring to a specific direction that has been established or assigned in a particular context.
Example: "In order to achieve the desired outcome, it is essential to follow a given direction throughout the project."
Alternatives: "a specified direction" or "a designated direction".
Exact(60)
In a given direction, the directional differentiation information around is summarized in a Directional Binary Pattern (DBP): (2).
The brain literally changes course when you prod it in a given direction.
The antenna can be designed to concentrate the radio energy into a beam like a searchlight and so increase its effectiveness in a given direction (see electronics).
Differentiation is about rates of change; for geometric curves and figures, this means determining the slope, or tangent, along a given direction.
Ellsberg's best answer to a governmental entity using leaks to push the White House in a given direction was to counter with a leak designed to push the White House in the opposite direction.
Both seeking to take the meeting's floor, to steer its innocence and idealism in a given direction, both eager to run back to their contacts and brag of enlisting the group, and each obstructed, largely, by the other.
C2: trains run on that network in a given direction.
In a book, she suggests, the author leads readers in a given direction.
* (p <0.05) and # (p <0.001) indicate significant difference across scaffold types for a given direction.
For a given direction, the first-order derivative Gaussian kernel is defined as (3).
Another useful parameter when considering ash dispersal is wind persistence towards a given direction.
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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