Hi,
I added some extra markings to your drawing. (Point A, length b, vector c and vector d that is perpendicular to c) Point A is the end of your original line. b is some length you decide.
First you need to figure out d. You can either do so by rotating c by 90 degrees with RotateVector or by instead getting the right vector from the world rotation of your first person mesh.
Now you multiply d by b, let’s call it db. You subtract db from A to get the start of the new line and add db to A to get the end of the new line.