Does anybody here understand vectors?

[Raziaar]

Both mathematically and geometrically.

I'm having an issue with this particular page for vector projection.

This is a page errata from the book's website that pertains to this page.

But as this is explained to me, I still don't understand it. It's not sinking in. All the other vector stuff prior to this thus far has sunk in.

 

[Dog--]

 

[Raziaar]

I loved vectorman. But he doesn't help me here.

 

[Dog--]

Loved?

 

[Avoidist]

Sadly vector-man had to go in a different direction. He never got to the point. He was a little off his axis.

I could do this all day people.

 

[Tyguy]

math is the work of the devil

(I don't understand vectors)

 

[Raziaar]

Sadly, he was negated and thus had to turn his life around.

 

[Dan]

Which part don't you get? Do you know the definition of the dot product? And I assume you know how cosine functions.

 

[Avoidist]

If you want to simplify the problem a little, I suggest setting ||n||=1 and working through it, starting off with simple problems first.

Solve mathematically:
1). What is the projection of v=(1,2,3) on n=(1,0,0)?
2). What is the projection of v=(1,2,3) on n=(0,1,0)?
3). What is v(perp) in (1) and (2)?
4). What is the projection of v=(1,2,3) on n=(3/5,4/5,0)?
5). What is the projection of v=(1,2,3) on n=(3,4,0)?

Ignore the cos(theta) stuff for now, it's just explaining why there is a dot product there.

Also if these questions make no sense ignore them completely, it's Saturday here and I haven't done this stuff in ages.

 

[Warped]

i sucked at math...sorry bub

also google FTW!?!?

 

[Raziaar]

Which part don't you get? Do you know the definition of the dot product? And I assume you know how cosine functions.

I guess the first part that throws me off is where it says let's solve for vparallel.

I am confused at how n can be expressed like that. I suppose what I need to do is go back to geometry to figure that out?

 

[Dan]

Something that may or may not help is thinking of n/||n|| as being a single entity of the normalized value of n. You are basically getting rid of the magnitude, and only leaving an arrow pointing in the direction of n with a magnitude of 1. So if you want something else to point in the same direction as n, you can just multiply a magnitude (v//) by n/||n||. You are basically keeping the direction of n, but stripping it of the magnitude of n and giving it the magnitude of v//.

 

[Avoidist]

What Dan just said.

 

[Krynn72]

Rasterized graphics is where its at yo.

 

[Kinslayer]

This is some of the worst notation I've ever seen with vectors.

 

[Avoidist]

If you're referring to the source text, it's the standard notation for printed material. The rest of us have to make do with dodgy html.

 

[Kinslayer]

If you're referring to the source text, it's the standard notation for printed material. The rest of us have to make do with dodgy html.

Is it really?

I learned it with completely different (and much better in my opinion) notation. Seems a lot less confusing the way I learned it. Then again I might be thinking of something else since it's been a while since I studied vectors.

 

[Raziaar]

Something that may or may not help is thinking of n/||n|| as being a single entity of the normalized value of n. You are basically getting rid of the magnitude, and only leaving an arrow pointing in the direction of n with a magnitude of 1. So if you want something else to point in the same direction as n, you can just multiply a magnitude (v//) by n/||n||. You are basically keeping the direction of n, but stripping it of the magnitude of n and giving it the magnitude of v//.

Okay, so it's like this then? It's taking vector 'v' and turning it into a unit vector by dividing it by the magnitude of v, and then stretching that vector out by multiplying it by the magnitude of v||? Well, order of operation precedence goes before that though I think, where vector n is multiplied by the magnitude of vector v||, and then divided by the magnitude of vector n.

Hrm.

I understand vector normalization, that part of this book made perfect sense. I guess when I saw that equation I didn't really think of that in my head.


EDIT: Oh shit, this dot product shit and stuff is into calculus bullshit. God dammit. I'm not much more advanced than basic trigonometry.

See, this is a 3D Math book for Games and 3d graphics.

EDIT 2: Man, why can't the book make it as easy to understand as this video!?

http://www.youtube.com/watch?v=0qMW4d8HwDw

Damn book still makes me scratch my head the way it's presenting it compared to how easily I understand it in the video.

 

[Minister]

Personally, I think books on Math completely overcomplicate everything.

I remember I hated vectors at college, that reservation for hate soon got replaced at Uni though.

I'm also with Kinslayer. Never seen vectors in that form.

 

[<RJMC>]

isnt vectors just straight lines that leads to one point to another?

so why dont you use a ruler and measure the distance?

 

[Mr Stabby]

It is direction dependant aswell.

 

[Reginald]

Less than a year ago I would have literally jizzed all over this question. Right now... I've forgotten everything.

:thumbs:

 

[CyberPitz]

Vectors are so easy, I'm not helping.

:arms:

 

[Insano]

Vectors are so easy, I'm not helping.

:arms:

Administer the smackdown, sir.

 

[mindless_moder]

This is some of the worst notation I've ever seen with vectors.

i completely agree , we never used that kind of notation when studying vectors. I think the book you're using assumes too much prior knowledge.

 

[Kinslayer]

EDIT 2: Man, why can't the book make it as easy to understand as this video!?

http://www.youtube.com/watch?v=0qMW4d8HwDw

Damn book still makes me scratch my head the way it's presenting it compared to how easily I understand it in the video.

NO. BAD.

He makes unnecessary approximations (should have just let cos(theta) as cos(theta) when finding it, instead of approximating THEN reapplying to cos(theta)).

You should always be as exact as possible until the end answer.

Otherwise, this guy uses the notation I learned. Hurray.

 

[Insano]

Otherwise, this guy uses the notation I learned. Hurray.

That's because he's using the notation for writing. In books (typed text), they use bold letters instead of a letter with an arrow above it etc.

That's just the way it is.

 

[Omnomnick]

I understand basic GCSE vectors, nothing this complex.

 

[Raziaar]

NO. BAD.

He makes unnecessary approximations (should have just let cos(theta) as cos(theta) when finding it, instead of approximating THEN reapplying to cos(theta)).

You should always be as exact as possible until the end answer.

Otherwise, this guy uses the notation I learned. Hurray.

Well, I know he approximated things, and I know that's bad, but the way he went about solving the projection still applies though correctly, doesn't it? Provided I don't approximate and only truncate at the very end.


Yeah, this book has the following notation:

Scalar Variables: lowercase roman or greek letters in italics
Vector Variables: lowercase letters in bold face
Matrix Variables: uppercase letters in bold face

 

[Insano]

Yeah, this book has the following notation:

Scalar Variables: lowercase roman or greek letters in italics
Vector Variables: lowercase letters in bold face
Matrix Variables: uppercase letters in bold face

Correct, as do all books I've seen so far.

When writing, you write down scalar variables in lowercase roman or greet letters, vector variables with lowercase letters with an arrow above them and matrix variables with uppercase letters with an arrow above them.

 

[Kinslayer]

Correct, as do all books I've seen so far.

When writing, you write down scalar variables in lowercase roman or greet letters, vector variables with lowercase letters with an arrow above them and matrix variables with uppercase letters with an arrow above them.

My IB book used the writing notation :|

 

[Dan]

It is really annoying to try to take notes using bold and italic fonts. My penmanship doesn't extend that far.

 

[DEATHMASTER]

Vectors in linear algebra are easy

 

[Raziaar]

Vectors in linear algebra are easy

Well, see... I'm learning these vector things without even having taken linear algebra. Linear algebra comes after trigonometry and calculus.

 

[DEATHMASTER]

yeah even that crap isn't needed for LA. It's easier. But I only recognize some of your notation, we only use them to an extent.

 

[Insano]

My IB book used the writing notation :|

Ah, weird. Is it an international used book, or a book your professor made himself in LaTeX?

 

[Kinslayer]

Ah, weird. Is it an international used book, or a book your professor made himself in LaTeX?

I'll answer that with the expanded version of the acronym IB:

International Baccalaureate

http://www.haeseandharris.com.au/book.asp?book=ibsl

^ That one.

Edit: It looks like it uses the bold text, actually. Hey, I guess I was wrong. Been forever since I've studied these things. Never seen the parallel and perpendicular notations, though (in general I have, just not in reference to vectors). The bold comes out a lot more clearly too.

 

[Eejit]

Lame, thought you meant disease or gene vectors.
Carry on.