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`

Find the direction cosines of the line which is perpendicular to the lines with direction cosines proportional to 1, -2, -2 and 0, 2, 1

the acute angle between two lines such that the direction cosines l, m, n of each of them satisfy the equations l + m + n = 0 and l^2 + m^2 - n^2 = 0 is

The direction cosines of the lines bisecting the angle between the line whose direction cosines are l_1, m_1, n_1 and l_2, m_2, n_2 and the angle between these lines is theta , are

Find the angle between the two lines whose direction cosines are given by the equation l+m+n=0,2l+2m-mn=0

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

The angle between the lines whose direction cosines satisfy the equations l+m+n=""0 and l^2=m^2+n^2 is

Find the angle between the lines whose direction cosines are given by the equations: 2l-m+2n=0 mn+nl+lm=0.

Find the angle between the lines whose direction cosines are given by : 2l-m+2n=0, mn+nl+lm=0 .