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`

Prove that the three lines drown from origin 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_1,n_1],[l_2,m_2,n_2],[l_3,m_3,n_3]]=0.

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

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

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

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

Show that the condition that tha concurrent lines with direction cosines (l_(1).m_(1),n_(1)),(l_(2),m_(2),n_(2))and(l_(3),m_(3),n_(3)) are coplanar is l_(1)(m_(2)n_(3)-m_(3)n_(2))+m_(1)(n_(2)l_(3)-n_(3)l_(2))+n_(1)(l_(2)m_(3)-l_(3)n_(2))=0

If three mutually perpendicular lines have direction cosines (l_1,m_1,n_1),(l_2,m_2,n_2) and (l_3 ,m_3, n_3) , then the line having direction ratio l_1+l_2+l_3,m_1+ m_2+m_3, and n_1 + n_2 + n_3 , make an angle of

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1