inst[['sc_zhat_ecef_x', 'sc_zhat_ecef_y', 'sc_zhat_ecef_z']] = np.cross(
        inst[['sc_xhat_ecef_x', 'sc_xhat_ecef_y', 'sc_xhat_ecef_z']],
        inst[['sc_yhat_ecef_x', 'sc_yhat_ecef_y', 'sc_yhat_ecef_z']],