import numpy as np
from numpy import ndarray

import solution


def get_cross_matrix(vec: ndarray) -> ndarray:
    """Get the matrix equivalent of cross product. S() in (10.68)

    cross_product_matrix(vec1)@vec2 == np.cross(vec1, vec2)

    Hint: see (10.5)

    Args:
        vec (ndarray[3]): vector

    Returns:
        S (ndarray[3,3]): cross product matrix equivalent
    """
    S  = np.array([
        [0, -vec[2], vec[1]],
        [vec[2], 0, -vec[0]],
        [-vec[1], vec[0], 0]
    ])

    return S

