Is there a method to "decompress" acceleration scalar?

Is there a method to "decompress" the acceleration scalar? For example, I am computing the scalar as:
$sqrt{a_x^2 + a_y^2 + a_z^2}$
where $a_x, a_y$ and $a_z$ are the components of the acceleration vector. If I have the scalar value (norm), is there a way to determine the $a_x, a_y, a_z$ components? A colleague mentioned using gyroscope or angular data, but did not know further.