Get angle from vector

arctan2(y, x) or if you want hard way...
First, normalize vector. This can be done with dividing vector with it's length.
Get length: l = √x² + y² Then normalize by dividing both x, y with length.
Now you have unit vector to work with, use arccos or arcsin to get it's angle.
If you use arccos, It's arccos(x)=θ and invert it depending on its y or x
let vecn = vec.normalized;
if (vecn.x > 0) {
  angle = Math.acos(vecn.y); //radian
} else {
  angle = -Math.acos(vecn.y);
}

Get vector from angle and scalar(length)

It's quite simple, as you already have it's scalar and angle.
x = cos(θ) y = sin(θ) Now, simply multiply that unit vector with scalar.