How to get the equation for a 3D line given 2 angles

Question

Given 2 angles (a1, a2), where a1 is the horizontal angle and a2 is the vertical, how can I use these two angles to get the equation/s of a line that passes through the origin.

ex: 0° x 0° / 180° x 0° = (x,y,z) (0,(-∞,∞),0)

Answer 1

Two points fix a line. Now we need one more other than the origin. Let's say the Cartesian coordinate is $(x,y,z)$. Let's just assume that the point has unit magnitude. Given the two angles, $(x,y,z)=(\sin a_2\cos a_1, \sin a_2\sin a_1, cos a_2)$. Now you can use the line equation.