def multiply_vectors_xy(u, v):
    """Element-wise multiplication of two vectors assumed to lie in the XY plane.

    Parameters
    ----------
    u : list
        The XY(Z) components of the first vector.
    v : list
        The XY(Z) components of the second vector.

    Returns
    -------
    list
        Resulting vector in the XY plane.

    Examples
    --------
    >>>

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