Here's the question you clicked on:
ParthKohli
Are standard basis vectors constant?
no, what do you mean
are vectors even important?
or better yet...is Math important?
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?
im thinking these are \(\hat i, \; \hat j, \; \hat k\) for some reason
http://tutorial.math.lamar.edu/Classes/CalcII/VectorArithmetic.aspx "Standard Basis Vectors Revisited"
Oh yes,\[\overrightarrow{i} = \langle1,0,0\rangle\]Sorry... messed up
still thinking that's supposed to be \(\hat i\)
OK, but is \(\hat{i}\) the same as \(\overrightarrow{i}\)?
\[\hat i = \; \text{positive x-axis}\]
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
\[\vec i \implies \text{vector}\] \[\hat i \implies \text{vector component}\]
I don't really get any of those, but thanks :P
Yeah... @hartnn that's right!
think of it somehow like this: i => x j => y k => z
\[\vec\imath=\langle 1,0,0\rangle\]\[\vec\jmath=\langle 0,1,0\rangle\]\[\vec k=\langle 0,0,1\rangle\]
+ i => positive x-axis -i => negative x-axis + j => positive y-axis - j => negative y-axos k => positive z axis -k => negative z-axis
That's a nice way to handle it! :)
can u imagine a vector along x-direction and magnitude = 1.......thats i|dw:1347180055694:dw|
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
that means i is a vector component for x j is a vector component for y k is a vector component for z
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
lol, thanks... I don't think I can really get it now. I'm not a genius :P
yes. vectors are hard to grasp
in polar coordinates the basis vectors change direction
btw... why are you so keen in learning new things all the time @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. :|
none of us is 12 years old.
I'm 13 lol, and I don't think that age makes a difference :)
the difference is 1 year
I mean that age contributes nothing to how much a person knows...
with age comes wisdom
Actually, I should be ashamed that it took me 13 long years do this all.
I think your time is better spent on learning mathematics than thinking about all this :-)
lol,so u wanted to know everything from birth!!??
eww @Ishaan94 learn math
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.
An average baby doesn't have the necessary IQ to do calculus.
WE MADE HIS IQ DOWN BY MAKING HIM PLAY WITH TOYS.
to learn calculus you need to know algebra. to know algebra you need to know arithmetic. to know arithmetic you need to know kinesthetics
In fact a playful childhood might help better in developing one's mind.
That's what YOU believe.
a baby is supposed to enjoy, not learn math ..... thats why we me him/her to play ....
if your theory is right @ParthKohli then i can confidently concur that online schools educates people very well
online schools miseducate people because they keep jumping from topics to topics; skipping fundamentals
that is also why you should not disturb the status quo
I'm... not.... jumping, right?
you are. you're trying to learn this without the necessary fundamentals
i think u are going fast just because u want to answer more questions here..
Yeah, I am, but I didn't skip algebra... and I didn't skip logarithms... not even trigonometry.
Thus, not leaving fundamentals.
How much time did you spend on Algebra, Trig?
however, you skipped topics
there's a reason they give 4 years to algebra
I would need a definitive answer.
But I have managed to do it early... nothing's really wrong!
it's not because people are slow-learners
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.
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
i think it's a false cause to study for OpenStudy rather than to study for academics
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. :-)
he still has other subjects though. math is not everything
I might be wrong person to discuss about getting grades in school. I never really payed much attention to grades.