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experimentX Group TitleBest ResponseYou've already chosen the best response.1
you know polar coordinate system right!!dw:1349364467374:dw
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Yes.. a little... But NOT in vectors!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
no they are just same.dw:1349364550790:dw
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
dw:1349364634178:dw
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Since it's related to sine, and cosine, it's not linear translation, right?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349364748021:dw
 2 years ago

experimentX Group TitleBest 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?
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
xi + yj? i and j are unit vectors
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yes ... and in cartesian coordinate?
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Huh?! Are they different??
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
Woops sorry ... polar coordinate??
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Well... Isn't it what I got stuck?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
\[ r \hat r + \theta \hat \theta\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
now we need to find the relation between \( \hat r , \hat \theta \) and \( \hat i, \hat j \)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
for that we know
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349365095537:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349365280570:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349365350758:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
how do we define unit vectors?
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
vector/length of vector?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yep ...
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349365586284:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
can you write the relation between \( \hat r \) and i,j
 2 years ago

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

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349365738630:dw
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Oh, should I express it in terms of theta?
 2 years ago

Callisto Group TitleBest 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!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349366033743:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
can you check page no 14 again?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
you got your first relation right?
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Eh.... I was about to say no, but then, yes :
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

Callisto Group TitleBest 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.. :(
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
sure till then i'll work out on the original methoddw:1349366641329:dw
 2 years ago

Callisto Group TitleBest 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.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349366770653:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349367409678:dw
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
So, they are the unit vectors?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349367720837:dw
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Right, your trick works :
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
PQ as a vector? or...?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yep. PQ
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349367904332:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
i hope you are understanding.
 2 years ago

Callisto Group TitleBest 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?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yep .. .cos C  cos D .. and ...
 2 years ago

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

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349368740990:dw
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Isn't that PQ something horrible??
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
lol ... no. Looks like i forgot cos C  cos D
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349369192240:dw
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Enough hint already!! (shhh!!~)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349369373117:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349369423357:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349369566965:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349369666573:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
**************************************************************************************************************************************************************
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349369888678:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1349369925726:dw
 2 years ago