Show that ` | (a_1l_1+b_1m_1, a_1l_2+b_1m_2,a_1l_3+b_1m_3),(a_2l_1+b_2m_1, a_2l_2+b_2m_2, a_2l_3+b_2m_3),(a_3l_1+b_3m_1, a_3l_2+b_3m_2,a_3l_3+b_3m_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

If l_1^2+m_1^2+n_1^2=1 etc., and l_1 l_2+m_1 m_2+n_1 n_2 = 0 , etc. and Delta=|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)| then

If l_1^2+m_1^2+n_1^2=1 etc., and l_1 l_2+m_1 m_2+n_1 n_2 = 0, etc. and Delta=|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)| then

If l_1^2+m_1^2+n_1^2=1 etc., and l_1 l_2+m_1 m_2+n_1 n_2 = 0 , etc. and Delta=|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)| then

If l_1^2+m_1^2+n_1^2=1 etc., and l_1 l_2+m_1 m_2+n_1 n_2 = 0 , etc. and Delta=|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)| then |Delta|=?

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|