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No it does not.

Look. the blade is at an angle.
You are moving it straight down.
Ergo, the blad itself is at an angle with the movement.

Now, if you decompose the vector of that movement into...

Wrong.
By inserting an angle, you create lateral movement. If you look at it from the razor's point of view: For every mm down, you go 0.x mm sideways.
Ergo there is lateral movement. You don't...