import numpy as np

def point_on_hypersphere(n, theta):
    """Unit vector on n-sphere using angle theta in first two dimensions."""
    v = np.zeros(n)
    v[0] = np.cos(theta)
    v[1] = np.sin(theta)
    return v

def normalize(v):
    norm = np.linalg.norm(v)
    return v if norm < 1e-12 else v / norm