I have some 3D vector data with the following parameters: X, Y, Z, v.X, v.Y and v.Z. I know the first three are just cartesian coordinates, but I don't know what the last three are, I just know they define the direction of the vector. Here are some of the values:

What do they mean? How can I use them to rotate vectors defined, let's say, along the X axis, to get to the correct direction? Thank you!
EDIT:
Maybe this helps: I initially asked that the direction is defined using
$\cos(\phi)\cdot\cos(\theta), \sin(\phi)\cdot \cos(\theta), \sin(\theta)$, but that's obviously not the case because the norm of the direction vector is not 1. I tried normalizing it, but then when I plotted the vectors using the extracted theta and phi, they didn't look correct. There's also a chance I'm not rotating around the correct axes...