def cross_vectors_xy(u, v):
    """Compute the cross product of two vectors, assuming they lie in the XY-plane.

    Parameters
    ----------
    u : sequence of float
        XY(Z) coordinates of the first vector.
    v : sequence of float
        XY(Z) coordinates of the second vector.

    Returns
    -------
    list
        The cross product of the two vectors.
        This vector will be perpendicular to the XY plane.

    Examples
    --------
    >>> cross_vectors_xy([1.0, 0.0], [0.0, 1.0])
    [0.0, 0.0, 1.0]

    >>> cross_vectors_xy([1.0, 0.0, 0.0], [0.0, 1.0, 0.0])
    [0.0, 0.0, 1.0]

    >>> cross_vectors_xy([1.0, 0.0, 1.0], [0.0, 1.0, 1.0])
    [0.0, 0.0, 1.0]

    """
    return [0.0, 0.0, u[0] * v[1] - u[1] * v[0]]
