If l1, m1, n1; l2, m2, n2; l3, m3, n3 are direction cosines of 3 mutually perpendicular lines then prove that the line whose directional cosines are perpendicular to l1+l2+l3, m1+m2+m3, n1+n2+n3 makes equal angles with them

If (l_1, m_1, n_1), (l_2, m_2, n_2)" and "(l_3, m_3, n_3) are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to (l_1+l_2+l_3,m_1+m_2+m_3,n_1+n_2+n_3) makes equal angles with them,

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 these are m_1n_2 - m_2n_1, n_1l_2 - n_2l_1, l_1m_2-l_2-m_1

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 these are m_1n_2-m_2n_2, n_1l_2-n_2l_1, l_1m_2-l_2m_1

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are direction cosines of two mutually perpendicular straight lines, then prove that the direction cosines of the straight line which is perpendicular to both the given lines are pm (m_(1)n_(2)-m_(2)n_(1)), pm (n_(1)l_(2)-n_(2)l_(1)), pm (l_(1)m_(2)-l_(2)m_(1))

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 these are m_1n_2-m_2n_1,n_1l_2-n_2l_1,l_1m_2-l_2m_1

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 these are m_1n_2 - m_2n_1, n_1l_2 -n_2l_1, l_1m_2 -l_2m_1

(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines. If the line, whose direction ratios are l_(1)+l_(2)+l_(3),m_(1)+m_(2)+m_(3),n_(1)+n_(2)+n_(3) , makes angle theta with any of these three lines, then cos theta is equal to