Answer:
The vector field is
Step-by-step explanation:
Consider two vectors a and b. Then, the vector b-a is a vector whose tail is at the tip of vector a and whose tip is at the tip of vector b. That is, it is a vector that points from the tip of vector a to the tip of vector b. To achieve the second restriction, we will take b as the 0 vector and to be the vector that points at point (x,y). Then, we have that at point (x,y) the vector that points to the origin is (-x,-y). Recall that given a vector (a,b), its magnitude is given by . Then, in this case we want that
Note that given a vector v, if we divided it by the cube of its magnitude, we get that
. Then, consider dividing the vector (-x,-y) by the cube of its magnitude. That is, consider the vector
Then,
.
Note that if (x,y) = (1,0) we get the vector (-1,0), which has magnitude one and that if (x,y) = (0,0) the field is not defined