Show that the three lines drawn from the origin with direction cosines proportional to 1,-1,1,2,-3,0 and 1,0,3 are coplanar

Prove that the three lines from the origin O, with direction cosines l_1,m_1,n_1; l_2,m_2,n_2;l_3,m_3,n_3 are coplaner if |[l_1,m_1,n_1],[l_2,m_2,n_2],[l_3,m_3,n_3]|=0

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

What is the angle between the lines whose direction cosines are proportional to (2,3,4) and (1,-2,1) respectively?

The angle between the lines whose direction cosines are proportional to (1,2,1) and (2,-3,6) is

What is the angle between the lines whose direction cosines are proportional to (2,3,4) and (1,-2,1) respectively

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to 1,-1,2 and 2,1,-1 are

A straight line with direction cosines (0,1,0) is

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