zaknenou

hhhhhhh homework in the summer ?
Although I know in Japan they give them such horrors

It sounds like you’re just beginning you journey in higher maths

I'm actually old and lurked in university stuff for a long time and dropped out of engineering in university and started with math all anew, yet at the same time I'm still a beginner.

Hmm. Where did the question in OP come from?

I don't exactly remember How I started thinking about the "distance between plane and a point formula", I think I stumbled upon it while organizing my old bookmarks. Tried to make a proof, and in the process that question came, and when I couldn't solve it on the fly I though like "it's so over for me". Then ChatGPT also got it wrong and was like "It's so over for mankind". And I ended up making this post to share my despair. Actually many answers were eye opening.

How first reading felt:

How the second reading felt at the beginning:

How it ended up:

What is {y∈V | O(y) = 0} ? If the plane doesn't pass through $0_V$ then how would that 0 be the image of some point ? Most likely you're using something from linear algebra that I didn't learn in my course (I didn't learn projection I think, only examples when learning matrices).

DUH! If this was math.stackexchange I'd choose this as answer

~~I tried again, I don't find mistakes in your statements, I just don't see how they make up for "instant in-mind proofs" for the problem~~ I think I see it now, nevermind. Your got a very good visualization for 3D CanadPlus. It seems so intuitive that "the set of points that map to H with orthogonal projection is a straight line", but do you happen to have a pocket proof for that ?

I couldn't make sense of the first paragraph, are you sure it is right ?

~~
fyi: the orthogonal projection of a point P into a plane is a point H of that plane such that for any other point A of the plane: (PH) is orthogonal to (HA). One might think that finding that "(PH) is orthogonal to (HA)" for one such point A of the plane is enough, turns out it is not.
luckily an easier criterion exists: H is the orthogonal projection of P if (PH) is parallel to n the normal to the plane.

retro computing was so chad

ADHD driven hard work could never disappoint huh?

But what was the advantage of QuickBasic? Weren't C++ and Javascript around at the time? I only hear about them in this context

https://www.youtube.com/watch?v=7rkiwtQjlVI

when I say forums, that includes math.stackexchange, please don't call it shitpost, people there are really something to say the least.