What does a vector field $f(r,θ) = (1,1)$ look like in polar coordinates?

Question

What does a vector field $f(r,θ) = (1,1)$ look like in polar coordinates $(r, \theta)$?

I was having some difficulty understanding what this looks like because i'm not familiar with vectors in polar coordinates.

would it be like this, you can get to any point on the plane by selecting an r and a theta, then at that point would have an orgin of a vector of radius 1 and angle 1 radian? which would make the vector field a set up parallel lines??

Answer 1

# Script Language: sagemath
#
#  it doesn't have a function to plot polar fields so i had to
#  create a wrappers to plot them using Cartesian vector fields.
x,y = var('x,y')

def f(x,y): 
    in_r = sqrt(x^2 + y^2)
    in_t = arctan2(y,x)

    out_r = 1
    out_t = 1 # angle measured from direction of r_in.

    x = out_r*cos(in_t + out_t)
    y = out_r*sin(in_t + out_t)
    return (x, y)

plot_vector_field(f(x,y), (x,-3,3), (y,-3,3), color='blue')