I’d like to edit my response. A few people pointed out the flaws in what I’d said and I see that I was wrong. The vanishing points would be different distances apart when objects rotate or change orientation. It’s easy to see this when you use a Station Point to find the vanishing points. I hope I haven’t caused too much confusion.

This may help you: Think of an infinite gridded plane, all vertical lines converge to the same VP no matter how large the plane is right? Infact no matter how big the plane is each square on that grid talks about each box that can be extruded from it where each individual box face the same direction and are aligned with this grid. (see first attached pic) Now imagine this infinite gridded plane turning in space, this would mean each box on that grid turns as well right? but then this means from a 1 point perspective where the second VP is off at infinity is now somewhere on the horizon line which would mean the distance between the VP has changed right? This is the keypoint though: Each box now on that grid share the same distance of VP. (see second pic) So essentially here are the keypoints: 1) If the boxes face the same direction they share the same VP and therefore share the same VP length. 2) If the boxes arent facing the same direction they wont share the same VP length. 3) This means VP is kind of fixed in space before drawing the box, where each individual angle of the box has their own unique set of VP somewhere on the horizon line. When it comes to focal length it basically means the distance between these infinite number of fixed VP change.

The simple answer is none of them is correct. But, here's the thing that get people confused, even though it's not correct, but you can still use the 'different vanishing points' technique in some limited cases. I guess a lot of people get confused with vanishing points. Vanishing points exist first, thus they affect the objects in the scene, but it's not the other way around. The position of the vanishing points cannot change just because the objects in the scene move or rotate. Even though there's no object in the scene, vanishing points will still exist. You see, the reason vanishing points themselves exist in the first place is because there's a camera shooting the scene, if there's no camera then there's no vanishing points. Thus the only thing that can change the position of vanishing points are when you move or rotate the camera (changing the camera position or angle), while the 'distance' between vanishing points can change when camera lens' focal length also change (you may have heard the term 50mm or 200mm in camera lens, that's the focal length). So in reality, there cannot be two different sets of vanishing points in one scene, leave alone different 'distance' between the vanishing points. There can only be one set of vanishing points and one distance in each scene, no matter how many objects you have in that scene. As many have pointed out below, the confusion starts when we can actually try to change the position of vanishing points, while maintaining the same 'distance', to portray objects rotation relative to the camera. There are some cases where you can successfully and correctly do that, but in some other cases it doesn't work. I've attached some 3D reference I made in Blender to show that, in that particular scene and camera angle, when the object rotation is counter clockwise, it does work, but when the rotation is clockwise, it just doesn't work.

The lengths don't stay the same and it's really easy to picture this. If you rotate the box enough, it will become 1 point perspective. 1 point perspective means that "the other vanishing point" is at an infinite distance. So the more the sides get parallel to the horizon, the larger the distance between P1 & P2. This is one of the difficulties with learning perspective. There's two ways to do it: 1. Calculate everything. 2. Practice and build intuition. I personally go with 2. especially since we have access to free 3D software. I'd suggest you fire up Blender or something and play with the camera set-up and focal length. And start with a cube. Good luck!

if you rotate the box clock wise the vp1 and vp2 should rotate clock wise as well, as long the degree is 90. in real world situation you have to make an educated guess because its not practical to use a protractor every time you draw. if you test it with a 3d software all your problems will be solved.

Yes, of course, that means the object is rotated.

Both are wrong, that's not how perspective works. Boxes with the same orientation will share the same Vps. Remember, parallel lines converge at the same Vanishing point in perspective. If you are trying to rotate a box, then No the length for the VPs do not stay the same for each rotated box. I suggest looking at Scott Robertson "How to Draw" page 25. The two vanishing points for a box should meet at 90 degrees on the Station Point. You rotate that 90 from the station point to rotate a box. The VPs for the rotated box will vary in length due to basic common sense geometry. You'll get it when you see it. hope this helps.

I’m pretty sure the distance between vanishing points should always stay the same. There’s a gif on Draw a Box that explains this https://drawabox.com/lesson/1/17/rotation (it’s a rotating box, where you can see the vanishing points moving with the box). I think the distance needs to remain the same or else it would be like using different camera lenses. For example, if you take a picture using a wider lens (the objects look more distorted), take a picture using a long lens and try to put them together, it’s very obvious there not part of the same picture (moderndayjames explains lenses briefly in one of his videos: https://www.youtube.com/watch?v=2XF5YuAK63I , about 4 minutes into the video). I tried to illustrate this using your example number 2, but more extreme. In my example, the green boxes look like they could be in the same scene and the blue boxes look like they could be in a different scene together. But together, the green and blue boxes have very different levels of distortions (because the vanishing points are not the same distance apart) so they don’t work together and make things look weird. Basically the lens stays the same, so the distance between the vanishing points stay the same. Hope this will be of some help! (ps I’m not sure if this is the best way to explain it, or if my explanation is 100% correct, but I’ve heard a lot of people who have much more experience talk about how the distance between vanishing points stays the same in a scene)