PreCalculus help

[Domi]

Can anyone explain 3D vectors to me?
And if you could also layout vector multiplication along with that original 3D thing, that would be dandy...

No seriously, I can't find anything about 3D vectors online, except for what comes up in programming. Then my question about vector multiplication is a little more direct, and if you think you can answer it I'll explain.

[morea]

hewligan to aisle 3, please... hewligan, aisle 3.

[Virgo Nightingale]

Is that what pre-calculus is for? I somehow passed that course in high school, but I can't for the life of me remember a thing about it.

[hewligan]

Dot product or cross product?

[Domi]

For now, dot product. It looks to me as if dot product explains 3D vectors, but I'm not sure. And then, if I'm right, what's the dot product of 3D vectors?

[morea]

hewligan, your brain is awesome. :D

[urstwile]

I wanna lick Hewligan's brain! :D

[hewligan]

Vectors work pretty much the same no matter how many dimensions you have (it's just really hard to imagine if you've got more than 3...).

If you take the dot product of a vector with itself, you get the square of the length of the vector. i.e. (aT = the transpose of T, which just means flipping it on its side)

a . a = aT a

= (ax ay az) (ax) = ax^2 + ay^2 + az^2 = (|a|)^2
(ay)
(az)

Where |a| is the length of a
(Damn it's hard writing maths in a forum... hope those spaces line up)

The dot product of two different vectors - i.e.

a . b

Gives the projection of a onto b times the length of b.

Diagram here: http://en.wikipedia.org/wiki/Image:Scalarproduct.gif

or a . b = aT b = ax bx + ay by + az bz = |a| |b| cos (C)

Where C is the angle between a and b.

Or, if the lengths of a and b are both 1 (and when dealing with direction, it's common to use vectors of length 1 or "unit vectors")

a . b = cos (C) iff |a| = |b| = 1

[frankster]

Yay! Go Hewligan! I was out eating a mahooosive omlette. I like omlettes more than Maths, so you can do all the maths and I'll feel guilt free about handling all the omlettes from now on.

[hewligan]

I'm not sure I'm getting the better end of this deal.

I mean, there's a reason why I'm a graphic designer...

[hewligan]

^^ Ooh, just noticed - that's post number 999...

Which means this must be number 1000! :D

Or, you know, clear evidence that I should get on with some work.

[budafist]

Congrats Hewligan on your 100th post!

[frankster]

I think you are supposed to get some kind of mexican bread product for your services to GDF at this point. I'm guessing they are flour not corn though, as Morea usually doles them out.

[hewligan]

Would these bready-corny products be parabolic in shape? :D

[frankster]

Sort of a bit hyperbolic paraboloidyish but not really.

edit: would you like pork, beef or chicken at the saddle point?

[hewligan]

Even maths sounds dirty when you say it Frankster.

I think I'm in love...

[frankster]

I have an 0800 number you can call if you want to talk about some relativistic quantum mechanics. ;)

[hewligan]

Oh baby, let me take the Hamiltonian of your wave function!

[frankster]

Oh dear, you made me snort tea out of my nose laughing. :D

[MikeTheVike]

hewligan, how do you remember stuff like that? I excelled in math when i was in school, but I'll be damned if I can remember anything now!

[D-Frag]

lol, you peeps crack me up

[hewligan]

hewligan, how do you remember stuff like that? I excelled in math when i was in school, but I'll be damned if I can remember anything now!

Well, a did a couple of degrees in physics at uni, which means I did a lot more maths than the rest of you (except Frankster who probably did about the same amount I did). So I've probably forgotten about the same proportion of the maths I learnt as the rest of you, I just learnt a lot more of it to start with ;)

[WannaBrie]

did maths > know maths = 0 I'm with Buda...I want to lick your brain Hewligan...My dad is an engineer and I just can't think like him, I totally admire anyone who can use both sides of the brain...

[Domi]

Thank God I was finally able to check back....

Anyho, Hewligan, thanks for the reply. It was pretty much what I've been seeing so far, thus, I'm still confused, but you did clarify some of my issues with this whole process.
What confuses me is how the length of a vector goes from the SQRT(x^2 + y^2 + z^2), in reference to pythagorean thereom, to just x^2 + y^2 + z^2. I thought the SQRT didn't distribute because of the parentheses. Does this change somehow and I'm just missing the whole step? Its that one little thing that keeps me from really seeing the rest of this.

[LeftBrain Artist]

Eh. I went as far as calculus in high school - but I don't remember any equations pertaining to vectors before that. That was, like, 15 years ago. I think I still remember the quadratic formula though. Not that I want to.

[CamarotaDesign]

Eh. think I still remember the quadratic formula though.
DONT YOU DARE #$*$@#ING POST THAT UNHOLY SIN!!!!

That and the "Two trains leave from different points and travel in opposite directions at X amount of time train 1 travels at X and train 2 travels at Y speed.. . . . . . " The mother of all evil math problems.

[frankster]

This is a nice straight forward explanation of things in chapters, even, dare I say it, with a bit of humour too...

http://chortle.ccsu.edu/VectorLessons/index.html


DONT YOU DARE #$*$@#ING POST THAT UNHOLY SIN!!!!

C'mooooooon Camarota! Whatcha gonna dooooooo? :eek: :p

http://upload.wikimedia.org/math/b/3/c/b3c2803cc3a8ae942dd1bd71a5391623.png

[urstwile]

Ooooh, Camarota, I think you've been served! :D

[CamarotaDesign]

:eek:Ahhhhhhh!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!

[frankster]

Oh my god Camarota! Are you ok? I didn't intend to give you an embolism! :o

(reminds me of the time we gave my great uncle Jack a surprise 80th birthday party):eek:

[hewligan]

Oh my God, Frankster - that's totally the hottest thing I have ever seen a woman do,

[CamarotaDesign]

Oh yes, I must say, despite that being scary, women with a sense of logic are hot! :D

[frankster]

I go weak at the knees for brainy guys. I'm sure it's down to my childhood adoration of Johnny Ball. Still can't figure out why I like ginger blokes though.

[LeftBrain Artist]

Oh yes, I must say, despite that being scary, women with a sense of logic are hot! :D

Especially if they've got huge tracts of land, too.

[hewligan]

http://imgs.xkcd.com/comics/certainty.png