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experimentXBest ResponseYou've already chosen the best response.1
you know polar coordinate system right!!dw:1349364467374:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Yes.. a little... But NOT in vectors!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
no they are just same.dw:1349364550790:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
dw:1349364634178:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
we know that we write (x, y) as our point. In polar coordinate we write (r, theta) < this means this is a vector space. you have been using it unknowingly.
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Since it's related to sine, and cosine, it's not linear translation, right?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349364748021:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yep. now let's go back to unit vector for a while. in cartesian how do you represent a vector?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
xi + yj? i and j are unit vectors
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yes ... and in cartesian coordinate?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Huh?! Are they different??
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Woops sorry ... polar coordinate??
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Well... Isn't it what I got stuck?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ r \hat r + \theta \hat \theta\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
now we need to find the relation between \( \hat r , \hat \theta \) and \( \hat i, \hat j \)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349365095537:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349365280570:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349365350758:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
how do we define unit vectors?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
vector/length of vector?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349365586284:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
can you write the relation between \( \hat r \) and i,j
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
unit vector of r = (xi + yj) / (x^2 + y^2) ? I know it's strange...
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349365738630:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Oh, should I express it in terms of theta?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
unit vector of r = (xi + yj) / (x^2 + y^2) \(= \frac{(rcos) \theta i +(rsin\theta)j}{r^2cos^2\theta+r^2 sin^2 \theta} \) \(= \frac{(rcos) \theta i +(rsin\theta)j}{r^2 } \) Hmm.. doesn't look good, sorry!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349366033743:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
can you check page no 14 again?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
you got your first relation right?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Eh.... I was about to say no, but then, yes :
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
for second relation there are many tricks. this is my favourite. polar coordinate is orthogonal coordinate system. \[ \hat r \cdot \hat \theta = 0\] so change \( \theta = \theta + 90 \) you will get second relation.
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Hmm, sorry!! OS is not loading properly here... And... please give me sometime to work it out first.. :(
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
sure till then i'll work out on the original methoddw:1349366641329:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Sorry... May I know what that e is?? I meant he wrote \(\hat e_\theta\) or \(\hat e_r\) there.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349366770653:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349367409678:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
So, they are the unit vectors?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349367720837:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Right, your trick works :
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
PQ as a vector? or...?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349367904332:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i hope you are understanding.
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
PQ (vector) =\(r (cos(\theta +d\theta) cos\theta )i + r (sin(\theta+d\theta) sin\theta)j\) Sumtoproduct formula?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yep .. .cos C  cos D .. and ...
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
\[PQ = r[cos(\theta+d\theta)cos\theta] i + r[sin(\theta+d\theta)sin\theta]j\] \[=2rsin(\theta+\frac{d\theta}{2})sin\frac{d\theta}{2}i +2rcos(\theta+\frac{d\theta}{2})sin\frac{d\theta}{2}j\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349368740990:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Isn't that PQ something horrible??
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
lol ... no. Looks like i forgot cos C  cos D
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349369192240:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Enough hint already!! (shhh!!~)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349369373117:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349369423357:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349369566965:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349369666573:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
**************************************************************************************************************************************************************
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349369888678:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1349369925726:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
similarly for theta dw:1349370057135:dw
 one year ago