How to make the dihedral angle of space, the distance from point to surface, and the angle between straight line and surface?

Generally speaking, if it is a simple geometric figure, the dihedral angle is easy to find. The common and basic methods are

A point passing through one surface (called M-bar) is perpendicular to the other surface (the intersection with the other surface is called O-bar), and the intersection of these two surfaces passing through O-bar is vertical (the vertical foot is called H-bar). The triple vertical theorem can be used to prove that the angle MHO is the dihedral angle of these two surfaces.

Sometimes, you can take the intersection of these two faces as the perpendicular of the intersection line, which is the definition of dihedral angle ... but this is rare, because the point given in the title or the special point you can find does not intersect the intersection line at one point ... but you should know that there is such a very clever time in this situation.

Of course, the vector method is the most strongly recommended, because there are many problems, and you can't directly find the dihedral angle. Even if you want to find it, you probably have to fill the shape, or even if you find a lot of auxiliary lines, it is inconvenient to find the geometric relationship. Vector method has no such problem at all. No matter how complex the geometry is, the vector method is completely brainless, so just calculate it carefully. Many times, vector method is definitely more time-saving than geometric method (anyway, so far, I haven't heard anyone say that vector method is a waste of time except your teacher). I think geometric method is something to improve ability, or it can be called cultivating mathematical sentiment. As far as the exam is concerned, the vector method should be able to do it all over the world ~ ~ Come on ~ ~ After all, math still needs more questions to feel ~ ~