anonymous
  • anonymous
I have to determine the field lines of the vector field f: R^3 --> R^3 defined by: f(x,y,z) = ((( x / ((1+z^2)*(x^2+y^2)),(y / ((1+z^2)*(x^2+y^2)))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
I have attached the assignment the one I wrote in the top is wrong, the right one is: f(x,y,z) = ((( x / ((1+z^2)*(x^2+y^2)),(y / ((1+z^2)*(x^2+y^2)),0)
experimentX
  • experimentX
F = i x-comp+ j y-comp + k z-comp ... most probably

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anonymous
  • anonymous
what do you mean by comb?
anonymous
  • anonymous
I dont have to draw anything?
experimentX
  • experimentX
component ... this is going to be complicated figure.
anonymous
  • anonymous
I dont understand what component mean. How will the final result be like?
anonymous
  • anonymous
Im sorry Im not very good at English
experimentX
  • experimentX
in each point in 3-dimensional space put the value of that point, you get a vector ... and the set of such vectors in such point is a field ... try for one point
anonymous
  • anonymous
im afraid I still dont get it
experimentX
  • experimentX
f(x,y,z) = (x, x+y, x+y+z) --- for example let this be a function, your x-component is x, y component is x+y, and z component is x+y+z at point 0,0,0 you have 0i+0j+k0 = 0 do you have 0 vector a 0,0,0 at 1,1,1 you have 1i+2j+3k ... not dray it ... it's going to look like this
anonymous
  • anonymous
I have never seen an assignment like this regarding field lines. Usually I know how to solve them but this is completely different from what I useed to do
experimentX
  • experimentX
|dw:1332839808130:dw|
anonymous
  • anonymous
but how is it in my case?
experimentX
  • experimentX
draw at every point, you will get a field .... In your case it's going to be much work, i'm afraid ... the earlier example i provided was simple case
experimentX
  • experimentX
try putting values at few points like (0,0,0), (1,1,1) ... you will get the general picture
anonymous
  • anonymous
|dw:1332839916152:dw|
anonymous
  • anonymous
How do you know which points to use?
experimentX
  • experimentX
you can use any points. since it is going to be complicated, use such points so that your work will be simpler
experimentX
  • experimentX
okay i will try to generate using some software
anonymous
  • anonymous
Thank you very much.
anonymous
  • anonymous
I dont even understand this part: F = i x-comp+ j y-comp + k z-comp
experimentX
  • experimentX
your z-component is zero ... so i guess, you will get a field on xy plane
experimentX
  • experimentX
it's a vector notation (2,3,4) = 2i+3j+4k
anonymous
  • anonymous
oh i see that now
anonymous
  • anonymous
But what then?
experimentX
  • experimentX
okay, find the value at 1, 1, 1
anonymous
  • anonymous
If I take too much time will you be able to help me later?
experimentX
  • experimentX
not so sure .. i might not be online
experimentX
  • experimentX
Oo i got one example ... wait for a while
anonymous
  • anonymous
Im not going to be able to solve this.......
experimentX
  • experimentX
i am trying using a software
experimentX
  • experimentX
i shouldn't take long
anonymous
  • anonymous
I can wait
anonymous
  • anonymous
I appreciate your help very much
experimentX
  • experimentX
sorry didn't work for z=0
experimentX
  • experimentX
for F = [ x/((1+z^2)*(x^2+y^2)), y /((1+z^2)*(x^2+y^2)), z]; you get something like this
1 Attachment
anonymous
  • anonymous
Oh my god
experimentX
  • experimentX
if you can make them flat ... i mean parallel to x,y axis --- from their point of origin ... you will have your answer
experimentX
  • experimentX
damn whoever coded this ... didn't code complete
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
that is the only part I know how to do now
experimentX
  • experimentX
yeah ... put value of x,y,z 1 1 1
anonymous
  • anonymous
Okay I get i1/5 + j1/5 + 0 ?
experimentX
  • experimentX
do you know how to plot this ?? |dw:1332842444812:dw|
anonymous
  • anonymous
No I really dont
anonymous
  • anonymous
Hehe it's hard to see what is happing in the drawing
anonymous
  • anonymous
I understand it has to be 3-dimensional but I dont know how to get the coordinates
experimentX
  • experimentX
AB is your vector ... it starts from 1,1,1 ... with 1/5 along x-axis and 1/5 along y axis
anonymous
  • anonymous
And do I just choose what I want like when I plottet (1,1,1) ?
anonymous
  • anonymous
wdy did you draw 3 vectors?
experimentX
  • experimentX
yeah ... more points you choose more abstruse and more better the picture
experimentX
  • experimentX
no it's just one vector ... two are to illustrate how it's components work ... and as you can see they are bidirectional
anonymous
  • anonymous
I dont understand that
anonymous
  • anonymous
and can I choose coordinates like (1,-1,-1)?
anonymous
  • anonymous
how can I find where the vector starts on the graph?
experimentX
  • experimentX
it starts form the point where you choose earlier
anonymous
  • anonymous
how do I find that point; 1/5,1/5,0?
anonymous
  • anonymous
in the graph you made, is the axis going up z?
anonymous
  • anonymous
Im sorry for all these stupid questions but Im lost
anonymous
  • anonymous
but how will the actual field lines look like? With all the arrows (vectors) I suppose we dont have the field lines yet
experimentX
  • experimentX
z axis is going up, and your coordinate was 1,1,1 not 1/5,1/5,0
anonymous
  • anonymous
What di I get if I use (1,1,-1)?

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