I have 2 planes, of which I know the maximum dip and azimuth. Here I am defining the azimuth as the direction of the maximum dip. How would one calculate the intersection angle between these 2 planes?
I have seen a lot online about how to calculate the dip and azimuth from the equation of the plane, and also on how to calculate the intersection angle using the equations of each plane. However, I don't have the equation for each plane.
Is it necessary to first calculate the equation for each plane? If so, how do I do this?
If I understand your notation, the unit vector of maximum descent of a plane can be written as $$ (\cos\alpha\cos\theta, \cos\alpha\sin\theta, -\sin\alpha), $$ where $\theta$ is the azimuth and $\alpha$ is maximum dip. A horizontal unit vector perpendicular to that and lying along the plane can then be written as $$ (-\sin\theta,\cos\theta,0) $$ and the cross product of these two vectors gives the unit vector normal to the plane: $$ \hat n=(\sin\alpha\cos\theta, \sin\alpha\sin\theta, \cos\alpha). $$ The angle $\phi_{12}$ between two planes can be computed by the dot product of their normal vectors: $$ \cos\phi_{12}=\hat n_1\cdot\hat n_2= \sin\alpha_1\sin\alpha_2\cos(\theta_1-\theta_2)+\cos\alpha_1\cos\alpha_2. $$