Short and sweet.
How does one calculate a directional vector in 3 dimensions by knowing the magnitude of the vector and the rotations about both the x and y axis?
Short and sweet.
How does one calculate a directional vector in 3 dimensions by knowing the magnitude of the vector and the rotations about both the x and y axis?
Making the assumption of my comment, that your rotations are the angle between the $x-$ and $y-$axes, you can find the vector with the following hints.
Hints Let the vector being determined be $\vec{u}=[u_x,u_y,u_z]^T$.
You now have 3 equations with 3 unknowns, as $\|\vec{u}\|,\,\theta_x$ and $\theta_y$ are known.
Note: This vector will not be unique.