I have a system of quadratic equations:
$$\cos(\theta_1) = \frac{u_1\cdot u' + v_1\cdot v'+w_1\cdot w'}{\sqrt{u_1^2+v_1^2+w_1^2}\sqrt{u'^2+v'^2+w'^2}}$$
$$\cos(\theta_2) = \frac{u_2\cdot u' + v_2\cdot v'+w_2\cdot w'}{\sqrt{u_2^2+v_2^2+w_2^2}\sqrt{u'^2+v'^2+w'^2}}$$
$$\cos(\theta_3) = \frac{u_3\cdot u' + v_3\cdot v'+w_3\cdot w'}{\sqrt{u_3^2+v_3^2+w_3^2}\sqrt{u'^2+v'^2+w'^2}}$$
In which I'm trying to solve for $u'$, $v'$, $w'$ (all other quantities are known). Is there any standard approach for solving this system? Specifically something I could code in python? Thanks in advance