I have two spheres with origins $O_1 =(a_1,b_1,c_1)$ and $O_2 =(a_2,b_2,c_2)$ in cartesian co-ordinates respectively . A radial line is drawn with azimuth and elevation given by $\theta_1$ and $\phi_1$ for sphere 1. Similarly, another radial line is drawn with azimuth and elevation given by $\theta_2$ and $\phi_2$ for sphere 2.
How can I find the point of intersection of these lines? Can someone help me with this. I am thinking if they had the same origin, the point of intersection would be the origin. So, maybe they intersect now at $(O_1-O_2)?$.