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`

The direction cosines of two lines are 1, -2,-2 and 0, 2, 1. Find the direction cosines of the line which is perpendicular to both the lines,

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,

Find the direction cosines of the two lines which are connected by the relation l+m+n=0,mn−2nl−2lm=0

Find the direction cosine of line which is perpendicular to the lines with direction ratio [1, -2, -2] and [0, 2, 1].

The angle between the lines whose direction cosines are l, m, n and m-n, n-l, l-m is......

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

Find the angle between the lines whose direction cosines are given by the equation l + m + n = 0 and l^2 + m^2 - n^2 = 0.

The direction cosines of two lines are given by the following equations. 3l+ m + 5n = 0, 6mn - 2nl + 5lm = 0. Find the angle between them.

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

The angle between the lines whose direction cosines are given by l + m + n = 0 and l^2 = m^2 + n^2 is .....