Because vectors’ origin or the side where there is no arrow can be placed at the origin and scaled to have a magnitude of 1, any parallel vectors in space would have the same unit vector because they would point in the same direction after being moved to the origin. The unit vector has a magnitude of 1. When scaling a vector you simply need to divide it by its own magnitude to do so and move it to start at the origin. This is true for 2-D or 3-D. This can be done because vectors can be scalable and translatable.
Note, however, at times it is critical to compare the magnitude of vectors and you should not scale the vectors. For example, in eigenvector decomposition, which is useful for PCA, the loading plot’s vectors should not be scaled. All of the vectors relative magnitudes are important. You can multiply all of the vectors by any value you want and it would retain the same meaning, however.
Best wishes,
Pharmacoengineering.com