How Do You Sketch These Vector Fields in the XY-Plane?

[-EquinoX-]

Homework Statement

I am asked to sketch the following vector field in the xy-plane

(a) F(r) = 2r


(b) F(r) = -r/||r||3


(c) F(x,y) = 4xi + xj

Homework Equations

The Attempt at a Solution

Can someone please give me some hints on how to proceed

 

[lanedance]

hi EquinoX

first I would look at the direction and magitudes of the vectors & see if you can spot any symmetries

a good way to start is to sketch the vector at several points as well

 

[-EquinoX-]

yes but for F(r) = 2r this is a 3D vector field, so if I am asked to sketch it in an xy plane, do I just look at the i + j direction? and is 2r basically just 2xi + 2yj + 2zk?

because r is xi + yj + zk?

 

[lanedance]

Yeah i think that should do

r = sqrt(x^2 + y^2 + z^2) and in the xy plane z = 0, so this shouldn't affect your r anyway

 

[-EquinoX-]

so r = sqrt(x^2)i + sqrt(y^2)j ?

 

[lanedance]

sorry bit of confusion over notation
|r| = sqrt(x^2 + y^2 + z^2)

r = xi + yj + zk

 

[-EquinoX-]

I am asking 2r?