Let `l_i,m_i,n_i; i=1,2,3` be the direction cosines of three mutually perpendicular vectors in space. Show that `AA'=I_3` where `A=[[l_1,m_1,n_1] , [l_2,m_2,n_2] , [l_3,m_3,n_3]]`

If l_(1), m_(1), n_(1), l_(2), m_(2), n_(2) and l_(3), m_(3), n_(3) are direction cosines of three mutuallyy perpendicular lines then, the value of |(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3))| is

If A = [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] then Find A+I

The direction cosines of a line equally inclined to three mutually perpendiclar lines having direction cosines as l_(1),m_(1),n_(1),l_(2),m_(2),n_(2) and l_(3), m_(3),n_(3) are

A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}] and B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}] Where p_(i), q_(i),r_(i) are the co-factors of the elements l_(i), m_(i), n_(i) for i=1,2,3 . 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 then (p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2)) and (p_(3),q_(),r_(3)) are

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_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),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_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .

Find the direction cosines of the lines, connected by the relations: l+m+n=0 and 2l m+2ln-m n=0.

Find the direction cosines of the lines, connected by the relations: l+m+n=0 and 2l m+2ln-m n=0.

Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 are proportional to l_1+l_2,m_1+m_2, n_1+n_2dot Statement 2: The angle between the two intersection lines having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 is given by costheta=l_1l_2+m_1m_2+n_1n_2dot