Question

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)))

Answer 1

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)

Answer 2

F = i x-comp+ j y-comp + k z-comp ... most probably

Answer 3

what do you mean by comb?

Answer 4

I dont have to draw anything?

Answer 5

component ... this is going to be complicated figure.

Answer 6

I dont understand what component mean. How will the final result be like?

Answer 7

Im sorry Im not very good at English

Answer 8

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

Answer 9

im afraid I still dont get it

Answer 10

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

Answer 11

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

Answer 12

but how is it in my case?

Answer 13

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

Answer 14

try putting values at few points like (0,0,0), (1,1,1) ... you will get the general picture