maths genius help?

Question

there is a theory telling that we can draw N perpendicular lines such that no lines parallel to each other.
how it could possible?? what happens to its imaginary line??

Answer 1

Well the theory is called (Euclidean) linear algebra, and I'll tell you what it says. First of all, it depends on where the lines are allowed to live. If you want to do this on a chalkboard, you have only two dimensions to work with. You get more room if you "draw" these lines in three-dimensional space. For example, if you look at the corner of a room, you can see it's where three perpendicular lines meet: the lines being 1) the line where the two walls meet and 2-3) the lines where the two walls meet the floor. There isn't such a good model for 4-dimensional space for us. Perhaps if you hold a pencil at that corner of a room for a minute, it's sketching a minute's worth of a line in the "time" direction, which will be perpendicular to the other three lines I mentioned. Sort of. You can see you have to use your imagination more than with three-dimensional geometry.

Anyway, you can translate your problem into linear algebra. It depends on the space the lines are in. What really matters is the direction of the lines, not whether they intersect, so you're really asking about the direction "vectors". And whether these vectors can be mutually perpendicular (which means they're not parallel). So the story goes that the biggest possible number of mutually perpendicular vectors is a *definition* of the dimension of the space. When we say our world is 3-dimensional, we *mean* that there are three essentially different directions, and when you write that up in mathematics that means this business about perpendicular lines.

So the upshot is to solve your problem you need N dimensions. And it would be difficult to explain how to *draw* in, say, 10 dimensions.

Answer 2

You can draw 2 such lines in 2-D space, 3 such lines in 3-D space, 4 in 4-D space, or, in general, n such lines in n-dimensional space (R^n). I don't know what you mean by 'its imaginary line'.

Answer 3

I usually could help you, yet because you're inquiring for each answer to thirty issues, that purely tells me you published the finished homework for somebody else to do for you. by using the time you finished typing those up, you need to've been accomplished with it. end being so lazy. those issues are so ordinary it is not even humorous. guess that makes each and every person a genius.

Answer 4

Do it in 3 dimensions, not in a plane.

Answer 5

do in 3 dimension and check at math boook