Are standard basis vectors constant?

- ParthKohli

Are standard basis vectors constant?

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- UnkleRhaukus

no, what do you mean

- lgbasallote

are vectors even important?

- lgbasallote

or better yet...is Math important?

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## More answers

- ParthKohli

In one of the examples, I noticed that they made a quick substitution for the following vectors:\[\overrightarrow{i} = \langle 0,0,1\rangle\]\[\overrightarrow{j} = \langle 0,1,0\rangle\]\[\overrightarrow k = \langle0,0,1\rangle\]So are vector i, vector j and vector k defined vectors?

- lgbasallote

im thinking these are \(\hat i, \; \hat j, \; \hat k\) for some reason

- ParthKohli

http://tutorial.math.lamar.edu/Classes/CalcII/VectorArithmetic.aspx
"Standard Basis Vectors Revisited"

- hartnn

i must be <1,0,0>

- lgbasallote

yes you are

- ParthKohli

Oh yes,\[\overrightarrow{i} = \langle1,0,0\rangle\]Sorry... messed up

- lgbasallote

still thinking that's supposed to be \(\hat i\)

- ParthKohli

OK, but is \(\hat{i}\) the same as \(\overrightarrow{i}\)?

- lgbasallote

\[\hat i = \; \text{positive x-axis}\]

- lgbasallote

no they are not

- ParthKohli

OK

- hartnn

and yes, i is defined as unit vector in x direction
j is defined as unit vector in y direction
k is defined as unit vector in z direction
and denoted by i^ as said by lg

- lgbasallote

\[\vec i \implies \text{vector}\]
\[\hat i \implies \text{vector component}\]

- ParthKohli

I don't really get any of those, but thanks :P

- ParthKohli

Yeah... @hartnn that's right!

- lgbasallote

think of it somehow like this:
i => x
j => y
k => z

- ParthKohli

Yeah, I do!

- UnkleRhaukus

\[\vec\imath=\langle 1,0,0\rangle\]\[\vec\jmath=\langle 0,1,0\rangle\]\[\vec k=\langle 0,0,1\rangle\]

- lgbasallote

+ i => positive x-axis
-i => negative x-axis
+ j => positive y-axis
- j => negative y-axos
k => positive z axis
-k => negative z-axis

- ParthKohli

That's a nice way to handle it! :)

- hartnn

can u imagine a vector along x-direction and magnitude = 1.......thats i|dw:1347180055694:dw|

- lgbasallote

one more thing you should know, the expression for vectors is given as
\[\vec A = x\hat i + y\hat j + z\hat k\]
or something like that

- lgbasallote

that means i is a vector component for x
j is a vector component for y
k is a vector component for z

- lgbasallote

so when you have \[\hat i\]
that means
\[\vec A = 1\hat i + 0\hat j + 0\hat k\]
so there's no value for y or z so it just lies on +x-axiis

- ParthKohli

lol, thanks... I don't think I can really get it now. I'm not a genius :P

- lgbasallote

yes. vectors are hard to grasp

- UnkleRhaukus

in polar coordinates the basis vectors change direction

- lgbasallote

btw... why are you so keen in learning new things all the time @ParthKohli ?

- ParthKohli

Because I can't stand the fact that I can't answer so many questions on the site, and there are people like you who know a lot. :|

- lgbasallote

none of us is 12 years old.

- ParthKohli

I'm 13 lol, and I don't think that age makes a difference :)

- UnkleRhaukus

the difference is 1 year

- ParthKohli

I mean that age contributes nothing to how much a person knows...

- lgbasallote

with age comes wisdom

- ParthKohli

Actually, I should be ashamed that it took me 13 long years do this all.

- anonymous

I think your time is better spent on learning mathematics than thinking about all this :-)

- hartnn

lol,so u wanted to know everything from birth!!??

- lgbasallote

eww @Ishaan94 learn math

- ParthKohli

We evolved with certain rules that made no sense. For example:
1) Babies are supposed to play with toys.
2) Adults are supposed to watch movies with stripping scenes.
3) Kids don't know anything.
I feel that it is *us* who evolved with these beliefs :)
a baby can do calculus as well, but we made the baby play with toys.

- lgbasallote

right

- anonymous

An average baby doesn't have the necessary IQ to do calculus.

- ParthKohli

WE MADE HIS IQ DOWN BY MAKING HIM PLAY WITH TOYS.

- anonymous

No. I don't think so.

- lgbasallote

to learn calculus you need to know algebra. to know algebra you need to know arithmetic. to know arithmetic you need to know kinesthetics

- anonymous

In fact a playful childhood might help better in developing one's mind.

- ParthKohli

That's what YOU believe.

- hartnn

a baby is supposed to enjoy, not learn math ..... thats why we me him/her to play ....

- lgbasallote

if your theory is right @ParthKohli then i can confidently concur that online schools educates people very well

- ParthKohli

lol

- lgbasallote

online schools miseducate people because they keep jumping from topics to topics; skipping fundamentals

- lgbasallote

that is also why you should not disturb the status quo

- ParthKohli

I'm... not.... jumping, right?

- lgbasallote

you are. you're trying to learn this without the necessary fundamentals

- ParthKohli

For example?

- hartnn

i think u are going fast just because u want to answer more questions here..

- ParthKohli

Yeah, I am, but I didn't skip algebra... and I didn't skip logarithms... not even trigonometry.

- ParthKohli

Thus, not leaving fundamentals.

- anonymous

How much time did you spend on Algebra, Trig?

- lgbasallote

however, you skipped topics

- ParthKohli

@Ishaan94 a lot

- lgbasallote

there's a reason they give 4 years to algebra

- anonymous

I would need a definitive answer.

- ParthKohli

But I have managed to do it early... nothing's really wrong!

- lgbasallote

it's not because people are slow-learners

- anonymous

Parth I think you should spend your time more on Algebra and Trig. Calculus isn't tricky. IMO doesn't even asks question from calculus. Get a good book on Algebra and start solving it.

- lgbasallote

agreed

- ParthKohli

g2g :) thanks all!

- lgbasallote

honestly @Ishaan94 don't you think kohli could be a valedictorian if only he tried using the time he spends doing calculus to just master algebra? if he has this kind of knowledge on calc, then he must hve spent a lot of time, enough to have made him a valedictorian

- lgbasallote

i think it's a false cause to study for OpenStudy rather than to study for academics

- anonymous

hmm I am not against Parth learning Calculus but the thing is Algebra could be a lot trickier than Calculus. So it's really important that one spends significant amount of time on Algebra.
As for academics I don't think 8th grade is really complex. He could still be a valedictorian. :-)

- lgbasallote

he still has other subjects though. math is not everything

- anonymous

I might be wrong person to discuss about getting grades in school. I never really payed much attention to grades.

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