The phase angle between the projection of U.C.M. on two mutually perpendicular diameter is,

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two mutually perpendicular lines show that the Direction Cosines of the line perpendicular to both of them are m_(1)n_(2) - n_(1)m_(2), n_(1)l_(2) - l_(1)n_(2), l_(1)m_(2) - m_(1)l_(2)

If l_1,m_1,n_1andl_2,m_2,n_2 are the direction cosines of two mutually perpendicular lines show that the d.cs. Of the line perpendicular to both of them are m_1n_2-n_1m_2,n_1l_2-l_1n_2,l_1m_2-m_1l_2