#help-7｜zen1thxyz

1 messages · Page 1 of 1 (latest)

echo fern
#

i'm not sure what set theory is 😅

hidden lotus
#

nvm

echo fern
#

elements of R^3?

#

would R^3 just mean dimension 3?

hidden lotus
#

Yes, basically

echo fern
#

so the general case would be something that you're describing?

#

and for the coplanar thing they're talking about, is that just using 3 vectors that share the same plane and doing the math out for the distributives ?

hidden lotus
#

Ordered Triples (because theyre conformed of 3 elements, with meaningful order) of Real numbers
v = (a,b,c) is in R^3

echo fern
#

i'm assuming for 1.2 we can do the same thing and just use any 3 vectors to show that they're not associative

hidden lotus
#

For 1.2 you can easily find a counter example

#

For 1.1 you cant

#

So you have to prove that the general case is true

echo fern
#

and we do that without rigid vectors but by the ordered triples you're talking about?

hidden lotus
#

rigid vectors and ordered triples i mentioned are two ways to represent the same object

echo fern
#

and we're just using that to show the general case is true with the distributive equations ?

hidden lotus
#

We cant use distributive properties because we are trying to prove they exist

echo fern
#

okay so we're trying to prove that those equations are true in the general case

#

and the general case is the ordered tripled you mentioned

#

how does the ordered triples thingy prove that the distributive is true?

hidden lotus
#

Because we define dot product and cross product using those too.

echo fern
#

what is an ordered triple?

hidden lotus
#

An object made by 3 elements, in order.

#

Say, (1,2,3) is an ordered triple

#

of 1 -> 2 -> 3

echo fern
#

okay so like

#

3,4,5

#

also ordered

hidden lotus
#

so, to start with, it isnt equal (7,4,2) because the elements arent the same
and isnt the same as (3,2,1) because its not the same order.

echo fern
#

or like -1, -2, -3 would also be ordered?

hidden lotus
#

Ordered has to do with the fact that the way they are presented is meaningful

#

not that they follow some order themselves

#

Bad example from me ig.

echo fern
#

hm what does it mean to be presented meaningfully

#

i don't know if it's a bad example i'm just trying to understand haha

#

sorry if it sounds like i'm nitpicking

hidden lotus
#

Points in the plane are also ordered pairs

image.png
#

if you read them as (x,y)
you have
Blue = (1,3)
Red = (2,2)
Grey = (2,1)

#

We usually say that "Points" are "position vectors"

#

but you could also draw them as arrows

#

Specially, when doing geometry with vectors, you assume that the vertices are like points, and there are vectors connecting them

image.png
#

This implies that theres some way to identify vertices to some arrow in space. (Coordinates)

echo fern
#

i guess i don't understand how this proves the distributive thing

hidden lotus
#

Im just giving you some introduction to the concept, has nothing to do with the problem itself.

echo fern
#

oh i see

hidden lotus
#

Just for a last thing

image.png
echo fern
#

okay i'm following so far

hidden lotus
#

If you say that the red point is at (1,2), and the vector connect the red point with the green is (1,3)

Then you can add (1,2) + (1,3)

#

Which works basically the same way as normal addition

echo fern
hidden lotus
#

(1,2) + (1,3) = (1+1 , 2+3) = (2,5)

#

tho, if you mean the one about the cross product, not at all

#

First i wanna see if you understand this, I just expect you to be able to see that these are simply 3 vectors, with (x,y,z) coordinates, without specifying.

dark aspen
#

r u saying that we plug in $\sqrt2 i$ for x?

plucky trellisBOT
#

Zen1thXYZ

1408302503971524649.png
dark aspen
#

yeah