Question

Vector valued functions

Can someone please please tell me what this is all about.

I don't understand the theorem, I am trying but I can't make sense of it:

http://screencast.com/t/V3vXqPSIkK5

Answer 1

@rishavraj

Answer 2

@Christos which step u got problem ??

Answer 3

in simple words...consider u got a vector 'r'
\[r ~=~x ~i ~+~ y ~j ~+~ z~k\]

and as the magnitude is constant .....
it means
\[\sqrt{x^2 + y^2 + z^2 } = const\]
\[x^2 + y^2 + z^2 = (const)^2\]

Answer 4

how can it not be constant ?

Answer 5

I mean, to me it looks like everytime the root is going to give a constant

Answer 6

I am kinda confused

Answer 7

like, how can it be constant, and how can it be varing instead of constant

Answer 8

now on taking derivative
\[2xx'~+~2yy'~+~2zz'~=~0\]

which is also equals to
\[2 r.r' = 0\]
so
\[r.r' ~=~0\]

Answer 9

u see in the question its mentioned tht the magnitude is constant

Answer 10

@Christos

Answer 11

Ok I think I got a bit of the theorem.. but do you know why he is replacing r1 and r2 into just r ? How does that prove the whole thing ?

Answer 12

@rishavraj

Answer 13

its nothing I believe ...its just mentioned to differentiate it in a understandable manner...I believe so

Answer 14

bcoz u see they are equal