Is it better to prove the dihedral geometry problem by traditional method or to find it by vector method?

1. Geometric method (traditional method)

The advantage of geometric method is that it saves a lot of calculation;

The disadvantage is that it is difficult to find the required dihedral angle for many problems, and the application scope of geometric method is relatively small.

2. Vector method (also called coordinate method)

The advantage of vector method is "brainless". You can write the coordinates of each point almost without thinking, and then find the vectors corresponding to two surfaces. The dihedral angle can be found by using the identity of vector point product.

The disadvantage is that the calculation is large and easy to make mistakes.

My suggestion is that if you can find the dihedral angle quickly, use the traditional method; If you can't find it, or it is difficult to find it, use the vector method. There is no absolute superiority or inferiority between these two methods.