**Task 1:** Write a function that finds, given a finite set of points in the plane and an integer $k$, the $k$ nearest neighbors of each point in the set using numpy's vectorized facilities.

**Task 2:** Apply your function to this set of points with $k=3$. Plot an arrow from each point to its $k$-nearest neighbors.

In [1]:

```
import numpy as np
P = np.array([[0,0], [0.2, 0.22], [0.1, -0.1],
[1,1], [1.1, 0.9], [0.8, 0.9], [1.1, 0.63],
[0.58, -0.1], [0.63, 0.1], [0.67, -0.3], [0.8,-0.23],
[0.8, 0.6]])
k = 3
```