def dot_vectors_xy(u, v):
    """Compute the dot 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
    -------
    float
        The dot product of the XY components of the two vectors.

    Examples
    --------
    >>> dot_vectors_xy([1.0, 0], [2.0, 0])
    2.0

    >>> dot_vectors_xy([1.0, 0, 0], [2.0, 0, 0])
    2.0

    >>> dot_vectors_xy([1.0, 0, 1], [2.0, 0, 1])
    2.0

    """
    return u[0] * v[0] + u[1] * v[1]
