Earlier you told me "hold a pencil up. A real pencil. I bet you can make perpendiculars in many directions, because the pencil is in a three dimensional space". Could you explain to me what do you mean by this? I try holding up a pencil and doesn't see anything.Thanks

No matter which way you old it, it is perpendicular to some plane.

Hold a book at different angles. Can you hold the pencil in such a way that it's perpendicular to the book, no matter which way you old it?

Yes.

the reason it is three dimensoinal, is so that it can go in every simngle way possible. i know that it seems like a lot at first but it is kind of simple...

Of course! I apologize if my previous explanation was unclear. When I mentioned holding up a pencil in a three-dimensional space, I was referring to the fact that our physical reality consists of three dimensions: length, width, and height.

When you hold a pencil in your hand, it is not just a two-dimensional figure on a page or a screen - it exists and occupies space in all three dimensions. You can think of it as a solid object that has a length (which you can see when you hold it in front of you), a width (which you can see when you view the pencil from the side), and a height (which you can see when you look at the top of the pencil).

Because the pencil exists in three dimensions, it has the ability to create perpendicular lines in different directions. Perpendicular lines are lines that intersect each other at a 90-degree angle. For example, if you hold the pencil vertically and draw a horizontal line across a piece of paper, the pencil can serve as a tool to create a perpendicular line to the horizontal line by drawing a vertical line.

Now, when you mentioned that you tried holding up a pencil and didn't see anything, it's important to note that the concept of creating perpendicular lines using a physical object like a pencil was just an analogy to help explain the concept of perpendicularity in three-dimensional space. In reality, the physical act of holding up a pencil may not result in visible perpendicular lines, as it depends on how you position the pencil and the surface you are using.

I hope this clarifies the concept for you! Let me know if you have any further questions.